An emotional Coco Gauff was able to recover and advance in the U.S. Open in New York on Thursday night. (AP photo)

NEW YORK (AP) — Coco Gauff kept wiping the tears welling in her eyes between points in her second-round match at the U.S. Open on Thursday night, trying to stay composed, trying to give herself a chance to win.

Gauff’s serving troubles were again an issue, just as they were two nights earlier, just as they’ve been for a while now. The two-time Grand Slam champion teamed up with a new coach recently to try to fix that aspect of her game, and while there clearly is still work to be done, Gauff did figure out how to stay in the tournament, beating Donna Vekic 7-6 (5), 6-2 in Arthur Ashe Stadium.

“Honestly, today was a tough match for me. But I’m just happy with how I was able to manage. It’s been a rough couple weeks,” Gauff said during her on-court interview, before pausing as she began to cry.

There were shouts of encouragement from spectators, and Gauff continued: “I’m doing this for myself, but I’m also doing it for you. No no matter how tough it gets inside, you can do it.”

Gauff won the U.S. Open in 2023 as a teenager, then added a French Open trophy this June. At the most recent Slam, Wimbledon, Gauff exited in the first round.

Her serving woes resurface from time to time, including when 19 double-faults contributed to a loss that ended her title defense in New York a year ago. She leads the tour with more than 300 double-faults this season — 23 in one match not long ago — and hired biomechanics expert Gavin MacMillan, credited with rebuilding No. 1-ranked Aryna Sabalenka’s serve, shortly before this U.S. Open.

In the first round, Gauff needed three sets to get past Ajla Tomljanovic, in part because of double-faults.

But like in that match, Gauff’s defense and superiority at the baseline carried her past Vekic.

Vekic, who beat Gauff at the Paris Olympics last year en route to the silver medal, took a medical timeout to have her right shoulder looked at late in the first set and was having plenty of serving woes of her own. She double-faulted 10 times.

In the first set, Gauff, a 21-year-old from Florida, had seven double-faults and lost four of her six service games, including to trail 5-4 — when the tears began — and then 6-5. But she broke right back each of those times and then was superior in the tiebreaker.

“I was just trying to tell myself to breathe and, honestly, just putting another ball in the court and just trying to remember the things that I do well,” Gauff said. “I don’t remember a lot of the end of the first set, to be honest, but, yeah, it’s kind of amazing that I was able to get out of that one.”

When Vekic sent a forehand long to end the set, Gauff’s mother rose from her seat, one row behind MacMillan, and shouted, “Come on! Let’s go!”

Gauff headed to the locker room to splash some water on her face and regain focus.

It worked wonders.

She reset herself, and the second set went much more smoothly: just one double-fault, zero service breaks, in front of a crowd that included star gymnast Simone Biles.

By the end, Gauff was in a much better mood, yelling while shaking a closed left fist when the match was won.

She had noticed that Biles was on hand.

“She helped me pull it out. I was just thinking: If she could go on a 6-inch beam and do that, with all the pressures of the world, then I can hit the ball. … It brought me a little bit of calm, just knowing her story, with all the things she went through mentally,” Gauff said. “She’s an inspiration, surely.”

OSAKA BACK ON TRACK

Naomi Osaka is back in the third round of the U.S. Open for the first time since 2021, the year after she won her second championship at Flushing Meadows.

She’s playing rather well at the moment, too, under the guidance of a new coach. Just don’t expect Osaka to weigh in on whether she feels as if she is ready to make another deep run at the place.

“Honestly, I don’t really know. I don’t make it my business to know anymore. I kind of just leave it up in the air,” the 23rd-seeded Osaka said after eliminating Hailey Baptiste 6-3, 6-1 in the second round in just 70 minutes Thursday. “For me, I realize that I’ve done everything that I could. I’ve trained really hard. I practiced really hard. If it happens, it happens.”

Venus Williams gets a US Open women’s doubles victory

Venus Williams earned her first win in a U.S. Open women’s doubles match since 2014 — and this time, her partner wasn’t younger sister Serena but Leylah Fernandez. The 45-year-old Williams, who recently returned to the tour after a 16-month absence, and Fernandez eliminated the sixth-seeded pair of Lyudmyla Kichenok and Ellen Perez 7-6 (4), 6-3.

What else happened at the US Open on Thursday?

Wimbledon champions Swiatek and Jannik Sinner both won — his victory was much more straightforward than hers. Swiatek had some trouble before getting past Suzan Lamens, a Dutch player ranked 66th who’d never appeared at a Grand Slam tournament until this year, by a 6-1, 4-6, 6-4 score. Sinner was just fine in a 6-3, 6-2, 6-2 win against Alexei Popyrin, who beat Novak Djokovic at the U.S. Open a year ago. In prime time, American Coco Gauff fought through serving issues and wiped away tears on the way to beating Donna Vekic 7-6 (5), 6-2, and on the men’s side No. 3 seed Alexander Zverev defeated Jacob Fearnley 6-4, 6-4, 6-4.

Who is on Friday’s schedule at the US Open?

Carlos Alcaraz, the 2022 men’s champion, and Jessica Pegula, the 2024 women’s runner-up, play their third-round matches in Arthur Ashe Stadium during the day session. Djokovic, owner of 24 Grand Slam titles, meets Cam Norrie in Ashe at night, followed by American Taylor Townsend — who got into a back-and-forth with her opponent, Jelena Ostapenko, after their second-round match — against No. 5 seed Mirra Andreeva, an 18-year-old from Russia.