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Denmark's Caroline Wozniacki returns a shot to Samantha Stosur of Australia during the first round of the U.S. Open tennis tournament, on Tuesday, Aug. 28, 2018, in New York.Frank Franklin II/The Associated Press

Former world No. 1 Caroline Wozniacki cruised past error-prone Samantha Stosur 6-3, 6-2 to reach the second round of the U.S. Open on Tuesday.

The Dane, who is the highest seed left in the draw after top seed Simona Halep fell in the first round on Monday, needed less than 90 minutes to get past the Australian, who committed 34 unforced errors and eight double faults.

The quick and comfortable win was a relief for the 28-year-old Wozniacki, who was able to get out of the blistering New York heat in relatively short order and save energy for her second-round match against Ukrainian Lesia Tsurenko.

"I’m just thinking I’m on the beach with a margarita in my hand,” Wozniacki said when asked about coping with the heat during an on-court interview.

The second seed showed no sign of the knee injury that forced her to retire midway through her match against Kiki Bertens at the Cincinnati Open earlier this month, moving well throughout the match.

The veteran Stosur, the tournament’s 2011 champion, briefly looked like she might deliver a second big upset in the women’s draw when she broke Wozniacki early in the first set, but the Dane broke right back to take a 4-3 lead she did not relinquish.

The second set was more straightforward as Stosur struggled to control her forehand on a hot day that sent balls flying and overheated fans into the shady sections of Arthur Ashe Stadium.

Two-time U.S.-Open finalist and New York resident Wozniacki advanced when Stosur double faulted on match point.

“I’m happy that I got through this one,” she said. “I’m going to celebrate the win today and tomorrow think about the next one.”

Earlier, former French Open champion Jelena Ostapenko sweated out a 6-4, 4-6, 7-5 win over German Andrea Petkovic to reach the second round.

With the thermometer pushing toward 38 C, the pair battled for 2 hours 18 minutes under a ferocious sun before the 10th-seeded Ostapenko ended the marathon on her fourth match point, sending the few remaining spectators at the Louis Armstrong Stadium court scrambling to find shade.

"Today was a very tough match. [Petkovic] was fighting for every point until the end,” said Ostapenko, who will meet American Taylor Townsend in the second round. “It is very humid, very warm and the match was more than two hours.”

Petkovic, having failed to qualify in Cincinnati and New Haven ahead of the U.S. Open, arrived at Flushing Meadows well rested. The 30-year-old needed all her reserves on a sweltering day that is sure to test the fitness of every player across the sprawling Billie Jean King National Tennis Center.

Ostapenko may have also benefited from an uninspiring buildup to the season’s final Grand Slam, crashing out in the first round at Montreal and Cincinnati to leave her fresh going into her opener.

In afternoon play, No. 4 seed Angelique Kerber showed that she has fully recovered from last year’s U.S. Open hangover by disposing of Russian Margarita Gasparyan 7-6(5) 6-3.

Champion in 2016, Kerber’s title defence last year ended almost before it began with the German suffering a 6-3 6-1 first round shellacking by Japan’s 46th-ranked Naomi Osaka.

That upset provided a sobering reminder that anything can happen at a grand slam and Kerber made sure she would not be caught with her guard down again this year as she took on a player making her U.S. Open main draw debut.

A three-time Grand Slam winner against an opponent sitting at 370 in the world rankings and making her first appearance in a major in more than two years would appear a mismatch but it was a contest Kerber approached in a business-like manner.

Despite the background Gasparyan, who has a WTA Tour title on her résumé, represented a potentially tricky first-round opponent, returning to the circuit this season after missing 15 months recovering from a career-threatening knee injury.

“This is the first time that we played against each other, and she was really hitting the balls really good, really clean,” Kerber said. “I knew that she was injured for a long time. ... Now she’s coming back.

“If she’s playing like this in the next weeks and months, for sure, she [will] soon [be] really high in the rankings.”

The Russian showed some of her potential and a fair amount of grit by battling to take Kerber to a first set tiebreak, but the Wimbledon champion kept her cool on a sweltering day on Louis Armstrong Stadium court to prevail 7-5.

The 23-year-old Gasparyan refused to wave the white flag and broke Kerber to open the second set, but the German broke back immediately to slowly seize control and wrap up the match.

“It was really not easy out there today,” Kerber said. “I think it’s one of the hottest days that I remember here.

“But at the end, when you’re out there, you just try to survive a little bit.”

On Tuesday night, Roger Federer improved to 18-0 in first-round matches at the U.S. Open and took one step toward a potential quarterfinal showdown against Novak Djokovic.

Dressed from head to toe in a plum-coloured outfit, the 20-time major champion delivered 14 aces and was never in any trouble during a 6-2, 6-2, 6-4 victory over 117th-ranked Yoshihito Nishioka of Japan at Arthur Ashe Stadium.

Federer saved the first eight break points he faced before finally faltering by pushing a forehand long on the ninth, losing serve for the only time while trying to close out the match at 5-2 in the third set. By then, the match was 1 hour, 45 minutes old – and it would last another seven minutes.

The No. 2-seeded Federer is seeking his sixth title at the U.S. Open – the first in a decade.

He would face 13-time major champion Djokovic if each wins three more matches.

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