NEW YORK — Facing much more resistance from the 90-degree heat and 50-percent humidity than from his outclassed opponent, Novak Djokovic figured he can count on cooler conditions during a night match at the U.S. Open his next time out.
The next foe? That could be Roger Federer.
Djokovic left the court at Arthur Ashe Stadium for a medical timeout — the second time during the tournament he’s sought help from a doctor because of harsh weather — during what would become an otherwise straightforward 6-3, 6-4, 6-3 victory over 68th-ranked Joao Sousa of Portugal on Monday in the fourth round at Flushing Meadows.
“I’m not 21 anymore. That was 10 years ago. I still don’t feel old. But at the same time, there is a little biological clock that is not really working in your favor,” the No. 6-seeded Djokovic told the crowd afterward. “Sometimes, you just have to survive.”
He reached the quarterfinals for an 11th consecutive appearance in New York as he bids for a third U.S. Open championship and 14th Grand Slam trophy. To add to his resume, though, he might need to beat Federer, who has won five of his men’s-record 20 major titles at Flushing Meadows.
Federer was scheduled to play 55th-ranked John Millman of Australia in the fourth round on Monday night. Like Sousa, Millman had never before made it this far at a Slam.
The other quarterfinal on the bottom half of the draw will be a rematch of the 2014 U.S. Open final: No. 7 Marin Cilic against No. 21 Kei Nishikori. Cilic, who beat Nishikori four years ago for his only major title, was a 7-6 (6), 6-2, 6-4 winner against No. 10 David Goffin, while Nishikori advanced by defeating Philipp Kohlschreiber 6-3, 6-2, 7-5.
Both Nishikori and Djokovic missed last year’s U.S. Open with arm injuries.
Asked Monday whether he thought during that time away about returning to the height of his powers, Djokovic replied: “I have imagined. I have hoped for. I have prayed for that.”
He improved to 28-0 at the U.S. Open against opponents ranked outside the top 50, and here’s another reason it wasn’t all that surprising the way things went against Sousa: Djokovic is now 5-0 in their head-to-head series, taking all 14 sets they’ve played against each other.
The heat, though, is much tougher on Djokovic, who showed the same blank expression, rosy cheeks and sweat-soaked shirt as during his first-round match last week. That was the first time in tournament history that the U.S. Open created an extreme heat policy for men’s matches — players can opt for a 10-minute break between the third and fourth sets — similar to what’s standard on the women’s tour, when there can be a delay between the second and third sets.
“It’s not easy,” Djokovic said, “to play in these kind of conditions.”
His match didn’t get to the point of a heat interruption, because he wrapped it up in straight sets, but that did come into play for a couple of women’s matches.
It was most striking during Lesia Tsurenko’s 6-7 (3), 7-5, 6-2 win against Marketa Vondrousova, in which both players seemed affected by the temperature and mugginess.
Tsurenko left the court for a health check after the first set and often leaned on her racket between points, saying later she felt dizzy at the Grandstand court, which doesn’t offer shade the way the tournament’s two bigger arenas do.
Vondrousova wasn’t all that sure Tsurenko had issues.
“I don’t think she was struggling so much,” Vondrousova said. “She was just acting.”
The 19-year-old Vondrousova, who said she dealt with cramping, certainly helped decide the outcome: Of Tsurenko’s 107 points, only 17 came via winners; 73 were her opponent’s unforced errors.
Also into the quarterfinals: 2017 runner-up Madison Keys of the U.S. and No. 20 Naomi Osaka of Japan. Osaka beat No. 26 Aryna Sabalenka 6-3, 2-6, 6-4 to earn her first trip to a Grand Slam quarterfinal. The 20-year-old Osaka was already the first Japanese woman to get to the fourth round in New York since 2004.
Keys overwhelmed No. 29 Dominika Cibulkova 6-1, 6-3 thanks to a 25-7 edge in winners and now will face No. 30 Carla Suarez Navarro of Spain. Suarez Navarro became the first player to beat five-time major champion Maria Sharapova in a U.S. Open night match, eliminating her 6-4, 6-3.
Sharapova won the 2006 title in New York, but she’s now lost in the fourth round in her past three appearances.