The chant rang out in cavernous Arthur Ashe Stadium on Monday at the U.S. Open before Coco Gauff's first service game of her first match of her first Grand Slam tournament as a defending champion: "Here we go, Coco! Here we go!"

Coming to Flushing Meadows off a series of early exits at other events, Gauff already was down 1-0 to Varvara Gracheva, having dropped the match's initial game at love by making four groundstroke errors. What followed was a tough, tight game, featuring 14 points across eight minutes and three break chances for Gracheva.

The important part, of course, was that Gauff saved all of those break points, claimed that game, and suddenly was in complete control on the way to a 6-2, 6-0 victory that not only put the 20-year-old American in the second round but also told her — and everyone else — that her game is in better shape than it appeared lately.

"The last couple of weeks were tough, and I was like, 'I have to do this and do that, but I don't have to prove anything to anyone except myself.' So ... (these) two weeks are just about proving all the expectations that I have on myself," the No. 3-seeded Gauff said. "I have many more years coming back here and I'm not going to win every year. Just that perspective and just having the belief that I can — but not the expectation that I should."

Day 1 at the year's last Grand Slam tournament went about as well as possible for Gauff and another young American featured in Ashe, 13th-seeded Ben Shelton, a semifinalist a year ago who beat 2020 champion Dominic Thiem 6-4, 6-2, 6-2. It was the last U.S. Open match for Thiem, who turns 31 next week and is retiring after this season.

"Obviously she plays with a lot of passion," Shelton, 21, said about Gauff. "You could tell that she cares out there. She's into it every time that she's on the court. I think that's something that the people love."

Gauff was not the only past U.S. Open champ on Monday's schedule: The night session in Ashe began with 2017 winner Sloane Stephens blowing a huge lead against Clara Burel and losing 0-6, 7-5, 7-5 after taking the first nine games, followed by Novak Djokovic — whose collection of 24 Slam titles includes last year's in New York — getting past Radu Albot 6-2, 6-2, 6-4.

Seeded women's winners included No. 2 Aryna Sabalenka, the two-time Australian Open champion who was the runner-up to Gauff a year ago in New York; No. 7 Zheng Qinwen, the women's gold medalist at the Paris Olympics earlier this month; No. 24 Donna Vekic, the silver medalist; No. 12 Daria Kasatkina; and No. 14 Madison Keys.

No. 9 Maria Sakkari stopped playing after one set because of an injured right shoulder. The highest-seeded man out of the bracket during the day session was No. 15 Holger Rune, who was eliminated by Brandon Nakashima of the U.S. 6-2, 6-1, 6-4.

Among the men's seeds advancing were No. 4 Alexander Zverev, the runner-up to Thiem four years ago; No. 6 Andrey Rublev; No. 8 Casper Ruud, the 2022 runner-up at Flushing Meadows; No. 9 Grigor Dimitrov; and No. 12 Taylor Fritz.

Zheng is enjoying a breakthrough season that began with a run to the final at the Australian Open in January and reached a peak when she claimed China's first Summer Games singles gold. Monday was difficult at the outset against 2019 French Open semifinalist Amanda Anisimova, but Zheng eventually came back to win 4-6, 6-4, 6-2.

"Everything starts at zero. You are not anymore the Olympic champion," Zheng said. "Just be humble and try to work, fight every single match, because if you don't fight, you have a big chance to lose."

That mirrors Gauff's approach as she returns to the site of her greatest triumph so far.

If she was trying to start from scratch after early exits in three events at the Paris Games — not that she wants to forget about that trip to France; Gauff wore a necklace with the Olympic rings during Monday's match — followed by a two-match skid on North American hard courts, Gauff did a good job of it.

This wasn't surprising to Gauff. Not at all. She knew she didn't play great in Toronto or Cincinnati in recent weeks. But she also could tell she was hitting balls well in practice.

"Usually that first round for me can sometimes set the tone for a tournament, whether you're playing well or not. ... I had a good mentality. Is this going to say I'm going to play great the next couple matches? Yes or no," Gauff said. "But I think the mentality I have going into this week will be there, and hopefully the execution stays there."

She only needed 66 minutes to win Monday, using some of her 10 aces to help erase all eight break points Gracheva accumulated, and compiling a 16-5 edge in winners.

"From the start, we kind of all knew that Coco was going to be an amazing player, and she's incredibly mature and carries herself in a way that I wish that I carried myself when I was her age," said Keys, 29, who lost to Stephens in the U.S. Open final seven years ago. "It's also very impressive how she's been able ... through all of the pressure and all of the expectation that's been put on her, continue to do as well as she has."

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