NEW YORK — Emma Navarro’s first Grand Slam semifinal will come at the U.S. Open against Aryna Sabalenka, someone trying to win her second major trophy of the year and third overall.

Navarro, an American who is seeded 13th, used a stunning turnaround to grab the last six games of her quarterfinal against Paula Badosa for a 6-2, 7-5 victory at Flushing Meadows on Tuesday, following up her upset of defending champion Coco Gauff.

“Sometimes you’re out in the court, and you can kind of picture yourself playing a third set. When I was out there, I didn’t picture myself playing a third set,” despite being down 5-1 in the second, Navarro said. “I felt like … I could come back and do it in two.”

Sure did.

There was no such drama in No. 2 Sabalenka’s 6-1, 6-2 win against No. 7 Zheng Qinwen, the gold medalist at the Paris Olympics last month, in a rematch of Sabalenka’s victory in the Australian Open final.

With Roger Federer in the stands, attending the U.S. Open for the first time since his retirement, Sabalenka displayed a typically powerful performance to get into the semifinals in New York for the fourth year in a row. In 2023, she was the runner-up to Gauff.

Sabalenka said she saw Federer in the crowd and figured he was there to watch Frances Tiafoe and Grigor Dimitrov in the match that followed hers.

“But still, I was like, OK, I have to play my best tennis so he enjoys it. I have to show my skills, you know, slice skills, come to the net and all that stuff,” Sabalenka, a 26-year-old from Belarus who’s known more for her power, said with a laugh.

She is trying to become the first woman since Angelique Kerber in 2016 to win the hard-court major titles at the Australian Open and U.S. Open. Sabalenka defeated Zheng in January for a second consecutive title at Melbourne Park.

“I just think the next time I play against her maybe I should hold a rally better and play a little bit more relaxed,” Zheng said. “Because today obviously I entered into the match with a lot of nerves.”

The opponents in the other women’s semifinal will be decided on Wednesday, when No. 1 Iga Swiatek plays No. 6 Jessica Pegula, and No. 22 Beatriz Haddad Maia takes on unseeded Karolina Muchova.

In the men’s quarterfinals Tuesday, No. 12 Taylor Fritz of the U.S. earned his first berth in the final four of a major, beating 2020 U.S. Open runner-up Alexander Zverev 7-6 (2), 3-6, 6-4, 7-6 (3).

Fritz had been 0-4 in Grand Slam quarterfinals but finally broke through against Zverev, the No. 4 seed he also defeated in the fourth round at Wimbledon.

“I’ve had a lot of looks at quarterfinals over the last couple of years and today just felt different,” Fritz said. “I really felt like it was my time to take it a step further.”

Tiafoe gave the Americans a third semifinalist when Grigor Dimitrov stopped playing because of an injury in the fourth set. Tiafoe was leading 6-3, 7-6 (5), 6-3, 4-1 and will play the 12th-seeded Fritz in Friday’s semis, guaranteeing the U.S. a men’s finalist in its Grand Slam tournament for the first time since 2006.

Navarro was three points from having to go to a third set against Badosa but won the next four points to stay alive, starting a stretch in which she captured 24 of the match’s last 28 points.

“Things weren’t looking great there in the second set, but just tried to be really tough, stick in there, make her hit one more ball,” Navarro said. “I felt like if I could scrap out a few longer points, maybe put some pressure on her, I felt like I could come back and maybe close it out in two sets. Happy with how I was able to do that.”

Navarro had never even won a match in the main draw of her home major before this year.

Badosa described herself as a “disaster” while dealing with the pressure of trying to reach her first Grand Slam semifinal.

“I never had the momentum in this match. I played four or five games OK. It was 5-1, but I never felt myself on the court,” Badosa said. “I lost, I don’t know, 20 points almost in a row. It’s very weird for me because I’m quite a consistent player, so I wasn’t expecting that either.”

Navarro also beat Gauff in the fourth round at Wimbledon before losing to eventual runner-up Jasmine Paolini in the next round, a 6-2, 6-1 rout in less than an hour.

But the 2021 NCAA singles champion for Virginia was ready for this matchup between New York natives, jumping on Badosa to win the first three games, then seizing the opening Badosa gave her late.

Navarro became the sixth player in the last 40 years to reach the U.S. Open semis without a previous main-draw victory in the tournament, a list that includes recent champions Bianca Andreescu in 2019 and Emma Raducanu in 2021.