Defending champion Simona Halep made it through to the French Open third round, where she joined three-time winner Serena Williams.

World number three Halep overcame illness to beat Poland’s Magda Linette 6-4 5-7 6-3 in two hours 11 minutes.

“I didn’t feel that great. Tomorrow I will sleep all day because I am a bit sick,” said Halep.

Earlier, 23-time Grand Slam champion Williams beat Japanese qualifier Kurumi Nara 6-3 6-2.

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Halep recovers from missed match points to win

Halep showed her intentions from the off, breaking her Polish opponent’s serve in the very first game with a stunning forehand winner.

Linette, 27, soon broke back to level the set at 2-2, before immediately losing on her own serve as Halep went on to hold for a 4-2 lead.

The next two games went against serve before Linette held and Halep secured the opening set in 49 minutes.

In the second set, Halep broke Linette’s second service game and looked set to serve out the match when she found herself 40-30 ahead at 5-4 up.

But stunning play from Linette, particularly on the forehand, frustrated Halep as the world number 87 defied her ranking to break back before winning the set.

Halep controlled the deciding set from the start, though, breaking Linette’s serve on three occasions as she went 5-1 up.

But unforced errors started to creep into her game as Linette mounted a comeback – Halep eventually wrapping up the set and match on a break.

She will next play Aleksandra Krunic or Lesia Tsurenko, whose match was suspended at 6-6 in the third set as darkness fell.

Meanwhile, there will be no French woman in the Roland Garros third round for the first time since 1986 after Caroline Garcia was knocked out.

Garcia, seeded 24th, was beaten by Russian qualifier Anna Blinkova 1-6 6-4 6-4.

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‘It’s going to get better’ – Williams happy after Nara win

Williams, 37, needed just one hour seven minutes to prevail over Japan’s Nara. The first set remained on serve for the first seven games, with world number 238 Nara proving a decent match for her opponent in the opening exchanges.

But Williams eventually broke 27-year-old Nara’s serve to move 5-3 ahead before serving out the set.

She dominated the second set, breaking Nara’s serve twice before serving out the match with an ace, having not dropped a point in the final game.

“I’m very serious when I play, but I’m happy,” said Williams.

“I have had a tough year since I twisted my ankle in Australia.

“It’s just been really tough after that. So everything definitely feels a little bit harder than normal, but at the same time, I know that it’s going to get better.”

On facing fellow American Sofia Kenin next, Williams said: “I know her game really well. She had a really great run in Australia, and I have been watching her.

“I think it will be a good match. She has a lot to bring to the table.”

‘I’ll remember it forever’ – Williams inspires Anisimova, 17

Elsewhere, fellow American Amanda Anisimova reached the third round after beating 11th seed Aryna Sabalenka 6-4 6-2.

She will next play Romania’s Irina-Camelia Begu, who defeated Karolina Muchova of the Czech Republic 1-6 6-3 6-4.

At 17, Anisimova is the youngest American to reach the third round at Roland Garros since Williams in 1999.

“She’s done so much for the sport,” world number 51 Anisimova said of Williams.

“She’s a huge inspiration to me. I really look up to her. That’s just great to be achieving stuff similar to her.

“Actually when I had a tough loss at the Miami Open – it was a really long match and I was super upset in the locker room – Serena actually came up to me and we shared a little bit of a chat.

“That was really nice of her, and I’ll remember it forever.”

Williams said: “I just needed to do that, and I know she’s super young. I really love all the new young players.

“It’s just so exciting. I feel like tennis has done so much for me, and to see a new generation come through is great.”

Meanwhile, Poland’s junior Wimbledon champion Iga Swiatek, also 17,knocked out 16th seed Wang Qiang of China 6-3 6-0 in under an hour.

Swiatek will play Puerto Rico’s Monica Puig after the Olympic champion beat Russian 21st seed Daria Kasatkina 6-3 6-1.

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World number one Novak Djokovic claimed a routine win over ‘lucky loser’ Henri Laaksonen to move into the third round of the French Open at Roland Garros.

Djokovic who won the 2016 competition, secured a 6-1 6-4 6-3 victory on Court Suzanne Lenglen in Paris.

He is aiming for his second Grand Slam title of 2019 after winning the Australian Open in January.

All of the top 10 seeded players in the men’s singles are into the third round after wins for six of them on Thursday.

Edmund retires from second-round match

• Serena Williams reaches third round by beating Nara
• Top seed Osaka survives scare to beat Azarenka
• Svitolina: Facing Muguruza, practising with Gael & romantic dinners

Laaksonen was beaten by Sweden’s Mikael Ymer in the third round of qualifying but took his place in the main draw after benefiting from withdrawals.

The Swiss, ranked 104th in the world, beat Spanish qualifier Pedro Martinez in the opening round to set up a first meeting with 15-time Grand Slam winner Djokovic.

The first set lasted only 23 minutes, but Laaksonen provided more resistance in the second, breaking Djokovic’s serve in the sixth game.

However, Djokovic twice broke Laaksonen’s serve in consecutive service games to take a two-set lead.

Djokovic, 32, will play unseeded Italian Salvatore Caruso, who knocked out France’s 26th seed Gilles Simon.

Thiem and Zverev safely through

Fourth seed Dominic Thiem, the runner-up last year, moved into round three with a 6-3 6-7 (6-8) 6-3 7-5 win over Kazakhstan’s Alexander Bublik.

Bublik three times opted to play underarm serves to disrupt Thiem’s rhythm, but could not beat the Austrian, who faces Uruguayan Pablo Cuevas after Britain’s Kyle Edmund pulled out with injury in the third set.

Asked about Bublik’s underarm serves, Thiem said: “It’s a good choice against players like us who are so far behind the baseline.

“For me it was tough. I had difficulties finding the right position. I didn’t practise [for] it but I just expect it from time to time. He won two out of three. Sometimes it’s quite a good tactic.”

‘We’ve seen so many underarm serves’ – analysis

Stuart Fraser, Times tennis correspondent, on BBC Radio 5 Live Sports Extra

Bublik has played underarm serves, taking some inspiration from Nick Kyrgios earlier this year. Someone made the point that they could be the first underarm serves on Chatrier since Martina Hingis 20 years ago?

This year is also the 30th anniversary of Michael Chang’s famous underarm against Ivan Lendl.

Someone like Rafael Nadal stands so far back, so there is an opportunity here and there if you get enough side-spin on it to play it. We’ve seen it so much this year.

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Round-up

German fifth seed Alexander Zverev beat Mikael Ymer 6-1 6-3 7-6 (7-3) to set up a meeting with 30th seed Dusan Lajovic of Serbia, who overcame French qualifier Elliot Benchetrit 6-3 6-4 6-4.

Argentine eighth seed Juan Martin del Potro survived a scare before beating Japan’s Yoshihito Nishioka 5-7 6-4 6-2 6-7 (5-7) 6-2.

There were also wins for ninth seed Fabio Fognini and 10th seed Karen Khachanov, who defeated Federico Delbonis and Gregoire Barrere respectively.

Fourteenth seed Gael Monfils, a French Open semi-finalist 11 years ago, knocked out fellow Frenchman Adrian Mannarino 6-3 6-4 6-4.

Monfils reached the third round at Roland Garros for an 11th time, equalling the French record held by Mary Pierce and Yannick Noah.

Diego Schwartzman, the 17th seed, lost 4-6 6-3 6-4 7-5 to fellow Argentine Leonardo Mayer.

French wildcard Antoine Hoang won 6-4 3-6 7-6 (7-5) 7-5 against Spanish 23rd seed Fernando Verdasco, who beat Britain’s Dan Evans in the first round.

Croat Ivo Karlovic, 40, who on Tuesday became the oldest player to win a match at Roland-Garros for 46 years, lost 6-3 6-4 6-7 (2-7) 6-3 to Australian Jordan Thompson.

World number nine Elina Svitolina, who has won 13 singles titles on the WTA Tour, will be writing columns for the BBC Sport website during the French Open, which runs from 26 May to 9 June.

The 24-year-old Ukrainian, who was at a career-high ranking of three last year, plays 2016 champion Garbine Muguruza in a blockbuster of a third-round match on Friday.

The two-time Roland Garros quarter-finalist talks about the strength of the women’s singles, facing Spanish 19th seed Muguruza and how practising with boyfriend – French world number 17 – Gael Monfils is improving her game.

There are many, many good players in a Grand Slam and I think these days the women’s game is at its highest level.

Players like Angelique Kerber and Caroline Wozniacki have already gone out, while Serena Williams, Naomi Osaka and Simona Halep didn’t have it easy.

That shows the depth of the women’s game and how strong the draw is.

It doesn’t matter if you are playing the person ranked 80th in the world or 20th – they are equally dangerous.

It’s impossible to predict how many players could possibly win Roland Garros because there are so many contenders.

But I don’t think too much about what is happening in the other parts of the draw.

And when a big name goes out there is not much talk in the locker room about it.

I only think about my part and mostly just the next opponent. If you look too far it can make you a little distracted and unfocused. What comes, comes.

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‘I need to react quickly to Muguruza’

After beating Venus Williams in the first round I have another tough challenge against Garbine Muguruza – someone who has won the Roland Garros title recently.

I’m not sure how that affects her – whether that brings more pressure on her or helps because she knows she can win here.

I don’t know because I have never been in this situation where I have won a Grand Slam and returned as the champion!

I imagine there are plusses and minuses but I try not to think about her situation – I try to think about myself.

Otherwise you have too many thoughts and it is useless to waste energy.

I have a good record against Garbine and have won six of our seven previous matches.

We have only played once on clay – in the 2017 Italian Open semi-finals – and she retired with a neck injury when I was leading 4-1.

But I don’t expect her to play any different to any other surface.

Garbine plays very early, she tries to dictate the point. So it is important for me to react really quickly and expect that.

‘Practising with Gael is fun and improves me’

I reached the third round in an unexpected way because my opponent Kateryna Kozlova – who I have known since we were children in Ukraine – had to withdraw from our match with illness.

An opponent pulling out doesn’t really affect me mentally. It comes, you have to react and adjust yourself.

So I had three hits on Wednesday instead.

Obviously I practised for my match and then when the match was cancelled I practised with Gael.

We were doing a doubles drill from the baseline where I’m attacking the ball and he’s defending – he’s obviously an amazing defender – so it was tough for me to make a winner.

He is too fit and too quick and too strong! So that’s why for me it is good.

I’m approaching and doing volleys and he is always there. It is good practice for both of us and it’s great fun.

Thankfully the loser doesn’t have to pay for dinner – but whoever loses gets a hard shot hit at their body!

After that practice I then played a set with my hitting partner later on Wednesday. I played my last match on Sunday so I have to be ready and keep my head focused for the next one.

Playing a set obviously isn’t the same as playing in the tournament match but that does help keep me a little in ‘match mode’.

In a Grand Slam you have to be fresh and ready and straight into the first point because you have to compete at the highest level straight away.

‘Relaxing and romantic dinners are important too’

Not playing because an opponent has pulled out means you definitely have time to be able to mentally relax a little as well.

We went for dinner with friends in the afternoon and then it was a quiet night because Gael played on Thursday.

We watch movies a lot but it is tough here in Paris to go shopping or whatever because Gael, as one of France’s biggest tennis stars, is obviously very famous here.

People recognise him and it is very difficult to have a calm walk through the Champs-Elysees, for example.

That means we don’t go out much, but on Wednesday we did go to our favourite restaurant near the Champs-Elysees – it is actually where we met!

We love that place. So it is a special place and brings back good memories.

Nowadays I would say I’m more relaxed when I’m on the practice court but still, of course, I’m very focused when I have to step on the tennis court.

It is important to do what makes you feel good on and off the court.

‘Playing on Chatrier is always special’

I wouldn’t say I have a favourite court in the world but I do love the show courts at Roland Garros – they are very special to me.

I always dreamed of playing at Roland Garros because I think it was the only one tournament they would show in Ukraine!

Whether I’m playing Chatrier, Lenglen or Simonne-Mathieu, it doesn’t matter to me – I really enjoy playing in all of them.

I thrive on playing on bigger courts, it gives you extra motivation. All the support you get on these courts helps you get through the tough moments and go again and again.

I’ve been told there have been a lot of empty seats on Chatrier at times – but I didn’t notice that when Gael played there on Tuesday.

It was not quite full, but it was a good crowd and he said afterwards the energy was amazing. It really fired him up.

I think the crowd size depends on the weather as well and also in the early afternoon, because in France lunch is almost like a holy thing!

If a stadium isn’t very full I don’t think about it too much, if it is a Grand Slam or a big tournament you have to push yourself.

Of course it is much better to play when the crowd is there, but playing on Chatrier is always special.

Elina Svitolina was speaking to BBC Sport’s Jonathan Jurejko at Roland Garros.