Karolina Pliskova can still win the US Open and keep her No. 1 ranking, thanks to a big comeback Saturday.

Pliskova fought off a match point in the second set and rallied to beat No. 27 Zhang Shuai, 3-6, 7-5, 6-4, to advance to the fourth round.

The runner-up last year needs to at least return to the final for a chance to remain atop the rankings when the year’s final major tournament is over, and it appeared for a while that the Czech wouldn’t get close.

But she stayed alive while trailing, 4-5, in the second set, then pulled out the third after receiving treatment from a trainer on her right forearm between sets.

‘‘Last Grand Slam of the season and knowing you played fine last year, you just want to play that good again,’’ Pliskova said. ‘‘I don’t feel like I'm playing that good again, but I'm still in the draw, actually, so I'm not going to be that sad.’’

The top seed on the men’s side also had to rally after dropping the first set. With the roof closed at Arthur Ashe Stadium because of rain, Rafael Nadal started to find the range with his punishing shots in the second set and beat Leonardo Mayer, 6-7 (3-7), 6-3, 6-1, 6-4, to reach the fourth round.

Roger Federer followed him onto Ashe to face No. 31 Feliciano Lopez.

Besides Pliskova, Wimbledon champion Garbine Muguruza and No. 4 seed Elina Svitolina are the other women who can still get to No. 1. Svitolina advanced to the round of 16 with a 6-4, 7-5 victory over Shelby Rogers.

Pliskova, who fell to Angelique Kerber in the 2016 final, would need to win the tournament if Garbine Muguruza reaches the semifinals and loses. If Muguruza advances to the final, Pliskova would be eliminated from contention for the WTA’s top ranking.

‘‘It’s not only about the points, but I just felt I really can play well here,’’ said Pliskova, who will next face American Jennifer Brady.

CoCo Vandeweghe, seeded 20th, outlasted 10th-seeded Agnieszka Radwanska, 7-5, 4-6, 6-4.

Nadal, Federer, No. 6 Dominic Thiem, and No. 9 David Goffin remain alive in their half of the draw. No. 12 Pablo Carreno Busta is the top seed in the other half of the draw, which will send a first-time Grand Slam finalist to the championship match next Sunday.

Thiem eased into the fourth round with a 7-5, 6-3, 6-4 victory over No. 30 Adrian Mannarino.

Thiem will next face No. 24 seed Juan Martin del Potro. The 2009 champion swept past No. 11 Roberto Bautista Agut, 6-3, 6-3, 6-4.

‘‘I think that bottom half of the draw is going to be surprising for one guy. But in the top half, you have Roger and Rafa, Dominic, as well, and they are favorites to win a Grand Slam title, for sure,’’ del Potro said.

Goffin won his match when No. 18 Gael Monfils retired with knee, back, and arm injuries with Goffin leading, 7-5, 5-1.

Also advancing were Philipp Kohlschreiber, seeded 33rd, a straight-sets winner over John Millman, and Alexandr Dolgopolov, who routed Viktor Troicki, 6-1, 6-0, 6-4.

Dolgopolov is into the fourth round for the first time since 2011 and will be the next opponent for Nadal, but was peppered in his post-match news conference about questions related to a match he was involved in recently in Winston-Salem, N.C., that’s under scrutiny because of unusual betting patterns.

The match is being assessed but is not yet under formal investigation, Tennis Integrity Unit spokesman Mark Harrison said earlier this week.

‘‘Obviously it’s disappointing, but not more,’’ Dolgopolov said. ‘‘If people want to write something, they write something. You can’t stop them from doing it. It’s just not under my control.’’

French Open women’s champ Jelena Ostapenko was ousted with a 6-3, 6-2 loss to Russia’s Daria Kasatkina.

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Fabio Fognini was kicked out of the doubles tournament and faces a possible permanent ban from all Grand Slam events after insulting chair umpire Louise Engzell with a vulgarity during his first-round loss in singles.

If the Grand Slam Board determines Fognini committed a ‘‘major offense,’’ he also could be fined up to $250,000 for violating the code of conduct.

Fognini, who was seeded 22nd in singles, was fined a total of $24,000 on Friday by the US Open — nearly half of his $50,000 prize money in singles — for unsportsmanlike conduct during his loss to Stefano Travaglia on Wednesday. Fognini was cited for three violations, carrying fines of $15,000, $5,000, and $4,000.

Fognini’s suspension went into effect immediately, so he was withdrawn from the doubles tournament, where he and countryman Simone Bolelli had advanced to the third round.

After they won their second-round match on Friday — but before any repercussions for what happened in singles had been announced — Fognini was asked about the possibility of being penalized.

‘‘When someone makes a mistake, they apologize. Accepted or not accepted, at this point that’s not up to me,’’ said Fognini, who is married to 2015 US. Open women’s singles champion Flavia Pennetta. ‘‘Everyone makes mistakes. Certainly, I've had bad days. And I will have others, like every human being.’’

Fognini and Bolelli won the Australian Open doubles title in 2015.

The board said the major offenses were under the sections of Article IV, dealing with ‘‘aggravated behavior’’ and ‘‘conduct contrary to the integrity of the game.’’ Violation of either section could lead to the permanent suspension from the four major tournaments and the $250,000 penalty.

The board said there would be no further comment until the process is completed. Fognini, known as a volatile player, was fined $27,500 by Wimbledon in 2014 for his outbursts during a first-round victory.