Defending champion Sloane Stephens beat two-time Grand Slam champion Victoria Azarenka 6-3 6-4 to reach the fourth round of the US Open in New York.

The American third seed broke twice in the first set and three times in the second at the Arthur Ashe Stadium.

Both players battled hard in the second set and Azarenka came from 3-1 down to lead 4-3 before the roof was closed.

The 25-year-old French Open finalist will face Belgian 15th seed Elise Mertens in the next round.

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“I just hung in there and battled as hard as I could to keep fighting. I was playing a former Grand Slam champion,” Stephens said. “She raised her level so I just had to stay in it.

“It felt like a night match with the lights on. I have never played under this roof before but it is super cool. It was unlucky for her but I was thankful for the break.”

It was Belarusian Azarenka’s first appearance at the US Open for three years, having missed the 2016 edition while pregnant and last year’s tournament because of a custody battle.

And the 29-year-old showed glimpses of the type of tennis that took her to the top of the world rankings in 2012 but was let down by 27 unforced errors.

Azarenka, runner-up here in 2012 and 2013, believes she can still add to her Grand Slam titles if she can put in a full off-season of training, which she has not managed in recent times.

“Trust me, I wouldn’t be sitting here if I didn’t believe that. I would be home doing a bunch of different things and being successful at those things, but I want to do this,” she said.

“At this stage, it’s a matter of one, two points, and today I just need to cut down my unforced errors and then everything is going to be OK.”

When Stephens takes on Mertens for a place in the quarter-finals, she will be hoping to avoid a repeat of their most recent encounter with the Belgian beating her 7-6 (10-8) 6-2 at the Cincinnati Masters earlier this month.

Mertens booked her place in the fourth round at Flushing Meadows with a 6-3, 7-6 (7-4) victory over Czech 23rd seed Barbora Strycova.

Also through to the next round is Ukrainian seventh seed Elina Svitolina, who overcame China’s Wang Qiang 6-4 6-4.

The 23-year-old will play Latvian 19th seed Anastasija Sevastova, who came from behind to beat Russia’s Ekaterina Makarova 4-6 6-1 6-2.

Maria Sharapova set up a third-round clash with former French Open winner Jelena Ostapenko after beating Romania’s Sorana Cirstea in New York.

The 22nd seed, who won the 2006 title at Flushing Meadows, thwarted a second-set comeback to win 6-2 7-5.

The Russian, 31, has a 21-0 win record in night matches at the US Open, recovering from a break down in the second set to finish after midnight.

“You’ve got to be crazy to be here after midnight,” she said to fans.

The five-time Grand Slam champion hit 10 double faults and could have stayed up later with world number 51 Cirstea two points from forcing a third set, but Sharapova broke her 28-year-old opponent twice to force the win.

“There’s a saying we use a lot: It’s not how you start, it’s how you finish,” she said.

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Latvia’s Ostapenko is seeded 10th for the tournament and the 21-year-old fought back to beat American Taylor Townsend 4-6 6-3 6-4.

“It only gets tougher from here,” said Sharapova, who suffered a 15-month doping ban in 2016.

“Being seeded in the 20s, you know you’re going to get tough draws. You know you’re going to play Grand Slam champions.

“[Ostapenko] is a competitor, a great opponent. I look forward to it.”

The US Open women’s draw has lost its top two seeds after Caroline Wozniacki suffered a shock second-round loss to Ukraine’s Lesia Tsurenko.

The world number two from Denmark has reached the US Open final twice but lost 6-4 6-2 to the world number 36.

World number one Simona Halep lost in the first round while Australian Open champion Wozniacki’s defeat by Tsurenko was her third early exit this month.

“She played the game I was supposed to play,” said Wozniacki, 28.

“This part of the season is usually a part of the season I really look forward to, one where I really play well.”

Meanwhile, fourth seed and former champion Angelique Kerber overcame a second-set wobble against Sweden’s Johanna Larsson to make the last 32.

The German, who had never lost a set in three previous matches with Larsson, eventually won 6-2 5-7 6-4.

Kerber plays Dominika Cibulkova next after the Slovak advanced despite a two-point deduction for returning late from a heat break.

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Temperatures at Flushing Meadows were once again high enough for organisers to apply their extreme heat policy, but Cibulkova was deemed to have taken longer than the permitted 10 minutes to cool down between the second and third sets in her match against Taiwan’s Hsieh Su-wei.

“[The umpire] told me I was one minute late. I’m getting two points’ penalty. You cannot be serious,” said Cibulkova, who won 7-6 (7-3) 4-6 6-4.

“It took me, I think, more than three minutes walking through the people, because there were so many fans and so many people. I couldn’t believe it.”

American Madison Keys, who lost last year’s final to Sloane Stephens, beat compatriot Bernarda Pera 6-4 6-1 to set up a third-round match with Victoria Azarenka.

Fifth seed Petra Kvitova got past China’s Wang Yafan 7-5 6-3, breaking late to seal the opening set after initially letting a 4-1 lead slip.

Kvitova, 28, next plays 20-year-old Belarusian Aryna Sabalenka, who won the New Haven title earlier in August.

Sabalenka beat 2010 runner-up Vera Zvonareva 6-3 7-6 (9-7) to reach the last 32.

She is joined by her compatriot Aliaksandra Sasnovich, who upset Russia’s in-form 11th-seed Daria Kasatkina 6-2 7-6 (7-3)

Sasnovich will face Naomi Osaka – who clinched her biggest career title at Indian Wells in March – after the Japanese beat Julia Glushko 6-2 6-0.