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 U.S. Open opponent, Zhang Shuai, 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 to become the youngest American to make it this far at the U.S. 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 meets 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 in Ashe this year after having never previously won a match at the biggest arena in Grand Slam tennis.

How loud was it?

“It got so racuous 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’s 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 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.

None of the eight women in action Sunday had ever been past the fourth round at Flushing Meadows; only two have reached semifinals at any Grand Slam tournament: Gauff and No. 5 Ons Jabeur.

Jabeur, a finalist at Wimbledon in July, was scheduled to meet No. 18 Veronika Kudermetova at night.

That was to follow the most-anticipated men’s match of Day 7: defending champion and top-seeded Daniil Medvedev vs. Wimbledon runner-up Nick Kyrgios. When they met last month on a hard court at Montreal, it was Kyrgios who won.

Whoever emerged from that would face No. 27 Karen Khachanov, who defeated No. 12 Pablo Carreño Busta 4-6, 6-3, 6-1, 4-6, 6-3.

The other quarterfinal on the top half of the men’s bracket is 2022 French Open runner-up Casper Ruud against 2021 Wimbledon runner-up Matteo Berrettini.

No. 5 seed Ruud made it to his first U.S. Open quarterfinal — and stayed in the hunt to attain the No. 1 ranking by tournament’s end — with a 6-1, 6-2, 6-7 (4), 6-2 victory over Corentin Moutet. Berrettini defeated Alejandro Davidovich Fokina 3-6, 7-6 (2), 6-3, 4-6, 6-2.

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 of 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 U.S. Open doubles champion — she and Sam Stosur beat Gauff and Caty 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, 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’s 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 sport of more than 20,000 folks in Ashe doesn’t hurt, either.

“She’s found a home there,” Dad said. “I hope she’s going to play there for the rest of the tournament.”

AP Sports Writer Dan Gelston contributed to this report.