Defending champion Sloane Stephens fought back from a set down to beat world number 134 Anhelina Kalinina and progress to the US Open third round.

The American third seed, treated for blisters in the second set, won 4-6 7-5 6-2 in two hours and 46 minutes.

She faces Belarus’ Victoria Azarenka next, after the former world number one beat Daria Gavrilova 6-1 6-2.

Meanwhile, 16th seed Venus Williams, 38, beat Italy’s Camila Giorgi 6-4 7-5 in an hour and 52 minutes.

It sets up a potential third-round meeting with sister Serena, who plays Carina Witthoft later on Wednesday.

Ukrainian seventh seed Elina Svitolina also progressed with a 6-2 6-3 win over Germany’s Tatjana Maria.

The 21-year-old will play the winner of the match between Qiang Wang and Irina-Camelia Begu in the third round.

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Having lost an enduring opener in an hour and two minutes, Stephens broke three times in the second set only to be pegged back to 5-5 by Kalinina after receiving treatment for blisters on her hand.

The 25-year-old eventually closed out the set and, despite going a break down in the first game of the decider, proved too strong for the 21-year-old Ukrainian, who was playing in the main draw of a Grand Slam for the first time.

Stephens, who said she had “two bites of sushi and a slushy” during the 10-minute heat break before the final set, bemoaned the conditions on Arthur Ashe Stadium.

“It was super hot,” she added. “I was sweating a lot and it was not ideal conditions, but I am happy to get through.

“I hope that I play a little bit better than today [in the next round], go out and compete hard.”

French world number 31 Alize Cornet was given a code violation for taking her shirt off on court during her US Open first-round defeat by Johanna Larsson.

Cornet changed her shirt during the break between the second and third sets, but realised it was back-to-front and quickly switched it on court.

But the chair umpire gave her a warning – despite male players being permitted to change their shirts on court.

Cornet lost 6-4 3-6 2-6 to Sweden’s Larsson in the searing New York heat.

On Tuesday, temperatures close to 38C (100F) at Flushing Meadows were made more stifling by humidity levels of over 50%, with five male players forced to retire due to heat-related issues.

The Women’s Tennis Association’s (WTA) rules state female players are not permitted to change their clothing on court, and instead must do it in a dressing room.

Male players regularly change their shirts on court at the change of ends.

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Conditions at the US Open were described as “dangerous” as five men had to retire from their first-round matches on Tuesday because of heat-related issues.

Temperatures close to 38C (100F) in New York were made more stifling by humidity levels of over 50%.

French player Julien Benneteau, who won on day two, said matches in the middle of the day should not have been played.

“They were lucky they only had retirements,” said the world number 60.

The conditions led to tournament organisers implementing an extreme heat policy in men’s matches for the first time.

Wimbledon champion Novak Djokovic, who said he “struggled” with the heat in his win over Marton Fucsovics, added that the physical issues affecting some players were “really sad to see”.

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Six players were forced to retire from matches on Tuesday, with the United States Tennis Association (USTA) saying five of the withdrawals – Italian qualifier Stefano Travaglia, Lithuanian Ricardas Berankis, Argentine Leonardo Mayer, Russia’s Mikhail Youzhny and Serb Filip Krajinovic – were “heat-related”.

For Youzhny it was a sad end to his final Grand Slam tournament, with the former world number eight set to retire from tennis next month at the age of 36.

The women’s WTA has an extreme heat policy for its players, unlike the men’s ATP, which has a discretionary rule.

USTA managing director Chris Widmaier said the decision to introduce it for the men was made after consulting its medical team.

The ruling offered a 10-minute break to both players after the third set and was taken if either or both wanted it.

The break took place in women’s matches between the second and third sets.

‘We were naked in ice baths’

Former world number one Djokovic and his Hungarian opponent Fucsovics were the first players to take a break after both suffered in the high temperatures.

The Serb revealed that they used the time to sit in cold baths together.

“Marton and I were in ice baths next to each other. We were naked in the ice baths and it was a quite wonderful feeling.”

“It wasn’t fun to play in the heat,” said Fucsovics, who lost in four sets. “I was dying after each point. It was too hot for tennis. It’s dangerous.”

Djokovic, who asked for a sick bucket to be put next to his chair in the second set, added: “There’s so much cramping going on. You don’t want to see that.

“You have to be fit, of course. I agree with that. But there are some conditions that are so extreme that, as fit as you are, you can’t just not feel it.”

The USTA said it would make a decision on Wednesday, when conditions are forecast to be similar, whether to implement the heat rule for a second time.

“We will be doing this on a case-by-case basis,” Widmaier added.

He said the show-court Arthur Ashe and Louis Armstrong Stadiums do not have air conditioning when the roofs are closed, although they may be shut overnight in an attempt to cool the courts.

Five-time Grand Slam champion Maria Sharapova held off a spirited fightback from Swiss veteran Patty Schnyder to reach the second round of the US Open.

The Russian defeated Schnyder – who, at 39, is the oldest player ever to make the main draw of a Grand Slam via qualifying – 6-2 7-6 (8-6).

The match was Schnyder’s first in a Grand Slam since she came back to tennis in 2015 having retired in 2011.

“I knew I was in for a battle no matter her story or my story,” said Sharapova.

“For her to come back and have the desire is really admirable. I’m just really happy I was able to win that last point.”

Sharapova, 31, will play Romanian Sorana Cirstea in the second round in New York.

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Schnyder, who reached the quarter-finals at Flushing Meadows in 1998 and 2008, said: “It actually doesn’t feel so special and it doesn’t feel like I’ve been gone for such a while. It has been part of my life for so long.”

In their first meeting in 10 years, world number 186 Schnyder was handed an early break by Sharapova – who was crowned US Open champion in 2006 – after the Russian made three double service faults in the opening game.

Serving did not improve on either side of the net with the first four games all breaks, before Sharapova held for the first time to take a 3-2 lead.

From there, the 22nd seed dictated the first set, taking it in 40 minutes, and looked to have eased through the second having built a 5-1 advantage.

But errors started to creep into Sharapova’s game allowing Schnyder to level at 5-5 before forcing the tie-break, in which Sharapova – who hit 23 winners but made 46 unforced errors – needed four match points to seal victory.

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