NEW YORK -- Coco Gauff and Naomi Osaka set up a high-profile showdown between two past title winners in the US Open's fourth round with victories Saturday.
"Everyone will be watching," Venus Williams said. "That's what tennis needs."
With her work-in-progress serve looking the best it has in this tournament, Gauff, seeded No. 3, 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 at Flushing Meadows for a fourth consecutive year.
Gauff, 21, will make 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, behind only Williams (17).
After two difficult wins under the lights at 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."
Osaka, meanwhile, advanced to her first fourth-round match at any major since the 2021 Australian Open by eliminating No. 15 seed Daria Kasatkina 6-0, 4-6, 6-3 at Louis Armstrong Stadium,
"It's been a really long journey," Osaka said during her on-court interview, "but I'm glad to be here now."
Their meeting Monday, with a quarterfinal berth at stake, is a rematch from 2019, when Gauff was a 15-year-old making her main-draw debut at Flushing Meadows and Osaka was the reigning champion.
Osaka won that one in straight sets, then consoled a teary Gauff on the sideline and encouraged her to speak to an Arthur Ashe Stadium crowd that was pulling for the young American.
Osaka, who was born in Japan and moved with her family to the United States as a kid, said jokingly to the Armstrong fans: "Can somebody come to the match and cheer for me? It's kind of tough playing an American here, but I hope you guys adopted me, as well."
Gauff has won three of their four head-to-head matches since that unforgettable night at Ashe.
"I remember it was a tough moment for me because it was a hyped-up match. ... I guess I put way too much pressure on myself, thinking I maybe had a chance in that moment to actually do something, which I definitely did, but I think it was just I felt more expectation than I should, than maybe belief," Gauff said.
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. Gauff 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."
During an interview with Sky Sports on Saturday, Gauff discussed what she had been going through when she played Vekic on Thursday, a match that saw her in tears in the first set.
"I think it was a panic attack," she told Sky Sports. "I've had them before off the court, but it's the first time it's happened on the court.
"I was just trying to calm myself down and breathe in the moment. That was kind of why I went to the bathroom after the first set, to reset. I wanted to get off the court. ... But I think for me I needed that to happen because now I realize how much people love me and how much I should love myself in those moments."
In both of her earlier outings, against Ajla Tomljanovic on Tuesday and Vekic on Thursday, Gauff fell behind 2-0. Against Frech, Gauff went up 3-0 before running into a hint of trouble: She 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 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."
In other women's singles results Saturday, 11th-seeded Karolina Muchova -- who beat Williams in the first round -- defeated No. 21 Linda Noskova 6-7 (5), 6-4, 6-2 to reach the fourth round, where she will face No. 27 Marta Kostyuk, a 3-6, 6-4, 6-2 winner over Diane Parry.
No. 2 Iga Swiatek battled back to beat Anna Kalinskaya 7-6 (5), 6-4 and will next meet No. 13 Ekaterina Alexandrova, who advanced to her third straight major round of 16 after breezing past Laura Siegemund 6-0, 6-1. Alexandrova won all six of her return games and has won 77% of her return games for the tournament, the only player at 70% or higher.
American Amanda Anisimova, the Wimbledon runner-up to Swiatek, reached the second week of the US Open for the first time, defeating Jaqueline Cristian 6-4, 4-6, 6-2. It had been the only major she hadn't made the round of 16 or better before this week.
Anisimova, the No. 8 seed, will face No. 18 Beatriz Haddad Maia, who needed only 70 minutes to defeat Maria Sakkari 6-1, 6-2.
ESPN's Simon Cambers, ESPN Research and The Associated Press contributed to this report.