NEW YORK: For the first time at this U.S. Open, Coco Gauff didn’t double-fault in her first service game. And for the first time, she didn’t get broken to begin things, either.

With her work-in-progress serve looking the best it has so far in this trip to Flushing Meadows, the No. 3-seeded Gauff turned in by far her most solid — and stress-free — performance Saturday, defeating No. 28 Magdalena Frech of Poland 6-3, 6-1 to reach the fourth round of a tournament she won in 2023.

“It’s been like an emotional week … but I think I needed those tough moments to move forward,” said Gauff, who will face four-time major champion Naomi Osaka on Monday for a berth in the quarterfinals. “I was putting too much pressure on myself.”

Osaka, who won titles in New York in 2018 and 2020, moved into the fourth round — a stage she last got to at any major at the 2021 Australian Open — with a 6-0, 4-6, 6-3 victory over No. 15 Daria Kasatkina.

Back in 2019, during Gauff’s first U.S. Open, when she was just 15, she lost to reigning champion Osaka in the third round. Afterward, Osaka consoled a teary Gauff and encouraged her to address the crowd.

After two difficult wins under the lights at night in Arthur Ashe Stadium, Gauff started Saturday’s schedule with an 11:30 a.m. match. With shade covering nearly half of the blue court on a cloudless morning, there were none of the tears or struggles that marked her earlier appearances during the week.

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