NEW YORK -- Coco Gauff raised a fist then wagged her right index finger, responding to, and riling up even more, a loud-louder-loudest Arthur Ashe Stadium crowd that was standing and screaming. Gauff's US Open opponent, Shuai Zhang, covered both ears with her hands to shield them from what she described later as a "boom'' of sound.

Gauff and her fans were reacting excitedly to quite a point, one in which the 18-year-old Floridian raced to her right for a defensive forehand then changed directions to sprint and slide into a backhand that drew a netted volley from Zhang. Just four points later, Gauff was a quarterfinalist at Flushing Meadows for the first time.

Gauff, the French Open runner-up in June, came back in each set to beat China's Zhang 7-5, 7-5 on Sunday and become the youngest American to make it this far at the US Open since Melanie Oudin was 17 in 2009.

"Here, I can't hear myself scream. Makes me want to do it more. I think I'm feeding off the momentum a lot. I enjoy it,'' said No. 12 seed Gauff, who will meet No. 17 Caroline Garcia of France on Tuesday. "New York is bringing out a side of me that I haven't had since I was 15, so it's nice.''

After trailing 5-4 in the opening set then 5-3 in the second -- which she was a point from losing -- Gauff was buoyed by spectators who cheered her every point and chanted, "Let's go, Coco," as the end neared. She improved to 4-0 at Arthur Ashe Stadium this year after having never previously won a match at the biggest arena in Grand Slam tennis.

How loud was it?

"It got so raucous in there that I got a headache. I had to take an Advil,'' said Gauff's father, Corey. "I kept pinching myself. I'm like, 'My gosh, all of these people here for my daughter.' You dream about this, but you never know if you're going to realize that. She was pumping herself up, and they responded to her. It sent chills up my spine.''

Zhang, at 33 the oldest woman to reach the fourth round, said it was more noise than she has ever heard at a match.

She praised Gauff's play, calling her "a superstar'' and adding, "Everything is very good. She's so much younger than me. Her energy is so much better. She's faster. She's powerful.''

They competed mostly from the baseline, and the longer the exchanges, the more success Gauff found. She claimed a 45-26 edge in points that lasted five or more strokes.

Garcia is coming off a hard-court title at Cincinnati, and she stretched her winning streak to 12 matches by eliminating No. 29 Alison Riske-Amritraj of the U.S. 6-4, 6-1

"I'm super excited, actually, to play Coco -- in U.S., in New York, quarterfinal of a Slam. It's great,'' Garcia said.

The other quarterfinal on that half of the women's field will be between Ajla Tomljanovic, the player who beat Serena Williams in the third round, and No. 5 Ons Jabeur, who was the runner-up at Wimbledon. Tomljanovic got past Liudmila Samsonova 7-6 (8), 6-1 at Louis Armstrong Stadium in a matchup between unseeded players, while Jabeur defeated No. 18 Veronika Kudermetova 7-6 (1), 6-4.

Tomljanovic is a 29-year-old Australian player who is now into her third Grand Slam quarterfinal after making it that far at Wimbledon the past two years. On Wednesday, Tomljanovic beat Williams in three sets in what is expected to be the last match of the 23-time Grand Slam champion's career.

In Gauff-Zhang, the whirring of the Ashe retractable roof being pulled shut accompanied the start of the second set because of showers that started soon after, and it took a while for the artificial lights to reach full strength. The match proceeded, even though it was rather dark -- and quite humid -- indoors.

Zhang started getting a bit better in the back-and-forth midway through the second set, and when she hit a backhand winner of her own, she broke to lead 5-3.

Last year's US Open doubles champion -- she and Samantha Stosur beat Gauff and Catherine McNally in the final -- served to force a third set and was a point away from getting there, but Gauff steeled herself and stood her ground.

That set point was frittered away when Zhang sent a backhand long. Gauff smacked -- what else? -- a down-the-line backhand winner for her third break point of that game, and she then delivered a good return to a corner that drew a long backhand to make it 5-4 and start a four-game, match-closing run.

Everyone has known how talented Gauff is for a while now. After all, at 15, she became the youngest qualifier in Wimbledon history in 2019, beat Venus Williams in the first round of the main draw and made it all the way to the fourth. There have been more steps along the way, more achievements (last month, she became the second-youngest doubles No. 1 in WTA history) and her ever-developing game (the most notable recent improvements were to her forehand and second serve) keeps carrying her closer to the top of the singles rankings and closer to a Grand Slam title.

And at this point, having the full support of more than 20,000 folks at Ashe doesn't hurt, either.

"She's found a home there,'' Corey Gauff said. "I hope she's going to play there for the rest of the tournament.''

The Associated Press contributed to this report.