That was before Nadal, Novak Djokovic, who has 21 Grand Slam titles, and Roger Federer, who has 20, began dominating men's tennis. Djokovic, who is 35, did not enter this US Open because is not vaccinated against COVID-19 and was not allowed to enter the United States; Federer, 41, has undergone a series of operations on his right knee and has not played since Wimbledon last year.

Now come the inevitable questions about whether their era of excellence is wrapping up.

"It signifies that the years go on," Nadal said. "It's the natural cycle of life." Either Tiafoe or Rublev will advance to a first major semifinal. Rublev, who is 0-5 in Slam quarterfinals, beat No. 7 Cam Norrie 6-4, 6-4, 6-4 earlier Monday.

Other men's matches on Monday's schedule: 2014 US Open champion Marin Cilic vs. No. 3 Carlos Alcaraz, and No. 11 Jannik Sinner vs. Ilya Ivashka.

The No. 1 woman, Iga Swiatek, covered her head with a white towel during one changeover after falling behind by a set and a break in her fourth-round match. She kept making mistakes, then rolling her eyes or glaring in the direction of her guest box.

Eventually, Swiatek got her strokes straightened out and moved into her first quarterfinal at Flushing Meadows by coming back to beat Jule Neiemeier 2-6, 6-4, 6-0.

"I'm just proud," Swiatek said, "that I didn't lose hope." The 21-year-old from Poland will face another first-time US Open quarterfinalist next. That's No. 8 seed Jessica Pegula, the highest-ranked American woman, who advanced with a 6-3, 6-2 victory over two-time Wimbledon winner Petra Kvitova.

The other women's fourth-round matches Monday were two-time Australian Open champion Viktoria Azarenka against two-time major finalist Karolina Pliskova, and No. 6 Aryna Sabalenka against No. 19 Danielle Collins.

Nadal won the Australian Open in January and the French Open in June. Then he made it to the semifinals at Wimbledon in July before withdrawing from that tournament because of a torn abdominal muscle; that does not go into the books as a loss, because he pulled out before the match.

Nadal competed only once in the 1 1/2 months between leaving the All England Club and arriving in New York while recovering from that injury. His play has not been up to his usual standards at the US Open, which he has won four times.

He tweaked his service motion, tossing the ball lower than he normally does so as not to put as much strain on his midsection while reaching with his racket. There were plenty of signs Monday that his serve is just not in tip-top shape: nine double-faults, a first-serve percentage hovering around 50%, five breaks by Tiafoe.

There were signs of trouble for Nadal earlier in the tournament. He lost the first set of his first-round match. Did the same in the second round, when he also accidentally cut the bridge of his nose and made himself dizzy when the edge of his racket frame bounced off the court and caught him in the face on a backhand follow-through.

In the fourth round Monday, the next-to-last break came for a 4-3 edge in the fourth set, when Nadal put a backhand into the net, and Tiafoe skipped backward toward the sideline for the ensuing changeover, his fist raised. Fifteen minutes later, Tiafoe broke again, and it was over.

When one last backhand by Nadal found the net, Tiafoe put his hands on his head. When he sat in his sideline chair, he buried his face in a towel.

"When I first came on the scene, a lot of people had limitations on what I would do. ... I wasn't 'ready for it mentally.' I wasn't 'mature,'" Tiafoe said. But these days, he added, "I'm able to just do me and do it my way and enjoy the game I love." This represents the latest significant step forward for Tiafoe, whose only previous trip to a Grand Slam quarterfinal came at the 2019 Australian Open — and ended with a loss to Nadal.

Tiafoe thanked a long list of folks who were in the stands, including his parents — they emigrated from Sierra Leone in West Africa and Dad worked as a maintenance man at a tennis facility near the US capital — his girlfriend and Washington Wizards All-Star guard Bradley Beal.

"To have them see what I did today means more than anything," Tiafoe said. "Today's an unbelievable day and I'm going to soak this one in, for sure."