NEW YORK – They were chanting her name Sunday in Arthur Ashe Stadium, as Coco Gauff contemplated what would be her final service game.

“It feels insane,” she said later in an on-court interview.

Just wait until Tuesday’s quarterfinals.

The No.12-seeded Gauff was a 7-5, 7-5 winner over Zhang Shuai and will meet No.17 Caroline Garcia, who defeated Alison Riske-Amritraj 6-4, 6-1.

Gauff, only 18, is the youngest American woman to reach the quarters here since 2009. Melanie Oudin was 17.

Here are three thoughts on what these two Round of 16 winners need to do to continue their success.

Coco Gauff

Don’t act your age

The win over Zhang was a triumph of youth over experience. Gauff was the youngest player left in the draw – and Zhang, 33, was the oldest.

This was Zhang’s 41st major draw, 28 more than Gauff. And yet, the American teenager was more poised in the difficult moments. Zhang broke her first service game to take a 2-0 lead, and Gauff broke her right back with two resounding forehand winners. It happened again when Zhang took a 5-3 lead in the second set – and Gauff came back to win the last four games.

Zhang has been to two career major quarterfinals – one fewer than Gauff. The 18-year-old has reached the Round of 16 at all four majors but, instructively, this is Gauff's first quarterfinal that didn’t come at Roland Garros.

Keep the ball in play

The numbers are pretty clear. Against Zhang, Gauff lost 13 more points than she won when rallies were confined to four strokes or less. When they went five or more, she was plus-19.

Garcia is an aggressive player, who likes to take big swings. Against Riske-Amritraj, she was standing inside the baseline for first serves and taking the ball as early as possible. She’ll be telling herself to be more patient against Gauff.

Gauff’s defense is so good that it sometimes hampers her offensive game. She recently said that she has to constantly remind herself to be more aggressive because she sometimes just rolls the ball back into the court and knows she’ll be able to track down the reply.

Serving for the match at 6-5, down 0-15, Gauff put on an incredible display of defense, sprinting from corner to corner and, eventually, compelling a weary Zhang to drop a volley into the net.

That needs to happen early and often against Garcia.

Ride the wave

Gauff is unquestionably the darling of these massive crowds at the Billie Jean King USTA National Tennis Center now that Serena Williams has headed off into retirement.

She jazzed up the Sunday crowd on Ashe with some pyrotechnics down the stretch, finishing with a swinging fist pump when Zhang’s last backhand found the net. Her excitement is contagious and, with another spirited, partisan crowd, she should use that in Tuesday’s match against Garcia.

With a chance to move into the Top 10 after the US Open, Gauff bears watching. Along with Garcia and No.1 Iga Swiatek, she’s among the favorites to win the title here. After reaching the French Open final earlier this year, she already knows what it feels like at the back end of a Grand Slam.

Caroline Garcia US OPen 2022

WTA/Jimmie48

Caroline Garcia

Keep serving the lights out

She had another clean match against Riske-Amritraj, striking eight aces and winning all nine of her service games. Entering the US Open, Garcia was second among Hologic WTA Tour players in service games won (.798) and break points saved (.672). Her numbers at the US Open are even better – 33 of 35 (.943) and six of eight (.750).

Against Gauff – a speedy, relentless defender – free points could tip the balance. Garcia leads all women with 312 aces this year, 26 of them coming here. She had eight against Riske-Amritraj, which helped her escape breaks in several instances.

"She already have some experience with the final in Roland Garros," Garcia said. "She’s aggressive but maybe from a little bit farther [behiind the baseline] than I am. Big serve, huge serve, very powerful. Moving great. Very athletic."

Monopolize that momentum

Technically, only Liudmila Samsonova – winner of 13 straight matches – is playing better right now. Garcia has won 17 of her past 18 matches, and the quality of those victories is unsurpassed. In Cincinnati, she knocked out three Top 10 players  (No.3 Maria Sakkari, No.7 Aryna Sabalenka, No.8 Jessica Pegula) on the way to the title. It was her first WTA 1000 win in five years.

Champions Corner: Garcia casts aside doubt to make history in Cincy

Since Wimbledon, the Frenchwoman has won 29 matches – the most on tour. She’s also won 12 straight matches, a streak that goes back to qualifying at Cincinnati.

Change the narrative – again

Coming into this US Open, Garcia had played in 41 previous Grand Slam singles tournaments – and reached a single quarterfinal, at Roland Garros in 2017.  And so, Garcia, who was through to the Round of 16 here for the first time has created another career precedent. And a second career major quarterfinal.

By dramatically changing her attitude, Garcia has been less volatile on the court and far more consistent.

"I never played on Ashe [against] a big American player, so definitely going to be the first time,” Garcia said. “As a French player, I know that in Roland Garros, the crowd, it can be loud and everything. Obviously I know it’s going to be on the other way around.

“I’m really looking forward to it. It’s a great experience. I will get myself ready. I will have my little team behind me. That’s the most important, the people you care about who have been supporting you. I’m not going to complain to play Ashe against an American girl in quarterfinal."

It’s worth noting that she had lost all three previous matches versus Riske-Amritraj, including earlier this year in Nottingham, and turned that trend around on a dime. She was 3-5 against Petra Kvitova and had lost their two most recent matches – and then defeated her in the Cincinnati final 6-2, 6-4.

The reason we bring this up is that Gauff holds a 2-0 head-to-head advantage over Garcia.  The victories both came in 2021, in Indian Wells and Doha. Although Gauff won four of five sets, two of them went to tiebreakers.