NEW YORK — Coco Gauff already was down a set on Day 1 of the U.S. Open when she found herself locked in a marathon of a 30-point, 25-plus-minute game to begin the second set. Sure, there still was plenty of time to come back Monday night in Arthur Ashe Stadium, but this felt pivotal.

The 19-year-old from Florida had lost her past two Grand Slam matches – including a first-round exit at Wimbledon last month – and did not want to leave quietly or quickly this time. With thousands of partisan fans getting rowdier by the moment, the sixth-seeded Gauff finally converted on her eighth break point of that game, and wound up beating German qualifier Laura Siegemund 3-6, 6-2, 6-4 and reaching the second round at Flushing Meadows.

Once she had the lead, the biggest frustration for Gauff was the way Siegemund would make her wait to play the next point. Siegemund repeatedly took her sweet time and, early in the last set, was warned by chair umpire Marijana Veljovic. Brad Gilbert, who is one of two coaches working with Gauff lately, shook his head at how long it took Veljovic to intervene, and his reaction drew a smile from Gauff.

But serving while ahead 3-0 in that set, Gauff had enough and went over to make her case.

“She’s never ready when I’m serving. … How is this fair?” Gauff told Veljovic. “I’m going a normal speed. Ask any ref here. … I’ve been quiet the whole match. … Now it’s ridiculous. I don’t care what she’s doing on her serve, but (on) my serve, she has to be ready.”

Gauff wound up dropping that game – but then not another. Later, Siegemund was docked a point for delaying, which put Gauff up 5-1. That prompted Siegemund to argue her case to Veljovic – “I can’t go to the towel anymore?” – and drew some jeers from the crowd.

There was another hiccup for Gauff toward the finish: She served for the match at 5-2 in the third, but double-faulted three times. Those were her only double-faults of the entire 2-hour, 51-minute match.

In the end, she held on, and it was Gauff’s 12th victory in 13 matches since the disappointing showing at the All England Club. This recent run includes the two biggest titles of the American’s career and a win over No. 1 Iga Swiatek.

Gauff and Swiatek could meet in the quarterfinals next week.

Looking ready for a serious defense of her U.S. Open title, Swiatek won Monday’s first match in Ashe – she needed all of 58 minutes to dismiss Rebecca Peterson 6-0, 6-1 – but otherwise, the going was rough for some of the highest-seeded players.

Holger Rune, of Denmark, returns a shot to Roberto Carballes Baena, of Spain, during the first round of the U.S. Open on Monday in New York. John Minchillo/Associated Press

The No. 4 man, Holger Rune, was bounced 6-3, 4-6, 6-3, 6-2 by the 63rd-ranked Roberto Carballes Baena; the No. 8 woman, Maria Sakkari,lost 6-4, 6-4 to the 71st-ranked Rebeka Masarova.

Sakkari said afterward she was bothered by the odor of marijuana in the air.

“The smell. Oh, my gosh,” Sakkari told the chair umpire in the first set. “It was weed.”

Rune had his own complaint – before the match.

The two-time major quarterfinalist, a 20-year-old considered part of the next generation of stars in men’s tennis, was not thrilled about being sent out to compete on Court 5, posting a map of the tournament grounds to help his supporters find the place.

“I just didn’t expect to play on that court,” Rune said afterward. “That’s obviously disappointing, but not going to blame the court on the loss.”

Other seeded players exiting included the No. 16 woman, Veronika Kudermetova, who lost to American Bernarda Pera 7-5, 6-4, and the No. 25 man, Alexander Bublik, eliminated by 2020 U.S. Open champion Dominic Thiem 6-3, 6-2, 6-4. Tenth-seeded American Frances Tiafoe, a 25-year-old from Maryland who reached the semifinal at last year’s U.S. Open, had little trouble in a 6-2, 7-5, 6-1, victory over wild-card countryman Learner Tien.

Thiem, who’s had a series of injuries, hadn’t won a Grand Slam match since the 2021 Australian Open, dropping seven in a row until Monday.

“It’s a pretty special victory. … Especially here at the U.S. Open,” Thiem said, “with all the past and all the memories I have here.”

The first round is played over Monday and Tuesday. The tournament lasts two weeks and wraps up with the women’s singles final on Sept. 9, and the men’s singles final on Sept. 10.