With her work-in-progress serve looking the best it has so far in this trip to Flushing Meadows, No. 3 seed Coco Gauff turned in by far her most solid — and stress-free — performance Saturday, defeating No. 28 Magdalena Frech 6-3, 6-1 to reach the second week of the US Open for a fourth consecutive year.

Gauff, 21, will be making her 16th appearance in the round of 16 at a major, breaking a tie for the second-most such appearances by an American woman before her 22nd birthday in the Open era.

After two difficult wins under the lights at night in Arthur Ashe Stadium, Gauff got the schedule started with an 11:30 a.m. match. — with shade covering nearly half of the court on a cloudless morning.

“It was kind of hard to see the ball,” Gauff said, “but overall, I’m happy with the way I played.”

Two days after she double-faulted seven times and dropped four of her six service games in the opening set against Donna Vekic, Gauff had four double faults total against Frech and won seven of eight service games. She put in 76% of her first serves while averaging 98 mph, with a high of 113 mph.

“It’s been an emotional week … but I think I needed those tough moments to be able to move forward,” Gauff said. “I was putting so much pressure on myself, but I’m really out here just trying to enjoy it and not focus so much on results, but the process, and I think today showed that I was really having fun out there.”

In both of her earlier outings, against Ajla Tomljanovic on Tuesday and Vekic on Thursday, Gauff fell behind 2-0. Against Frech, she went up 3-0 before running into a hint of trouble: Gauff slapped a second serve into the net to double-fault and get broken, getting Frech within 3-2, and soon it was 3-all after 26 minutes.

In the next game, Gauff led 40-love but wound up at 40-30 after shanking a forehand that landed 10 feet out.

Thousands of fans started yelling encouragement and clapping to try to help Gauff. She heard, looked around and clutched a ball for her next serve, vigorously shaking it. Gauff stepped to the baseline and delivered a 105 mph first serve that drew an errant return. Upon watching the ball land out, she leaned forward, clenched her left fist and screamed “Come on!”

That began a set-closing three-game run, and Gauff was on her way.

Her serve has become a major issue, which is why she brought aboard a biomechanics expert, Gavin MacMillan, who helped Aryna Sabalenka settle her serving yips and rise to No. 1 in the WTA rankings with three major championships, including in New York a year ago.

“I know this process would be up and down, so today was definitely a positive, and I hope it goes up from here,” Gauff said of the improvements to her serve. “I think for me I guess I’m more proud of the mental effort of things and trying to remember the things that we worked on in practice. Today I definitely think was a step in the right direction.”

Gauff’s title defense at the US Open in 2024 ended with a fourth-round loss in which she had 19 double faults. She has been the worst player on the women’s tour in that category this season and reached a low point with 23 in a victory at Montreal last month and 14 more in her next match.

In the wins against Tomljanovic and Vekic, Gauff totaled 18 double faults and lost 10 service games. What got her through those was the rest of her game: returning, defending and a clear superiority once the ball was in play.

Those last three areas were again strengths for Gauff. She broke Frech five times and was terrific whenever their baseline exchanges lasted more than four shots, taking 35 of those 51 points. She also made only 18 unforced errors and claimed the point on 10 of her 11 times at the net.

Gauff will face four-time major champion Naomi Osaka or No. 15 Daria Kasatkina on Monday for a berth in the quarterfinals. She is 3-2 in her WTA career against Osaka (1-1 in majors) and 0-3 vs. Kasatkina, though they have never played in a Slam.

In other women’s singles results Saturday, 11th-seeded Karolina Muchova defeated No. 21 Linda Noskova 6-7 (5), 6-4, 6-2 to reach the fourth round.

ESPN Research and The Associated Press contributed to this report.