NEW YORK >> While Roger Federer and Rafael Nadal hope to remain on track for a possible semifinal showdown, Karolina Pliskova avoided becoming the latest top woman to exit the U.S. Open.

The No. 1 seed from the Czech Republic rallied for a 2-6, 6-3, 6-4 victory over American Nicole Gibbs on Thursday to reach the third round.

Fourth-seeded Elina Svitolina also advanced with a 6-4, 6-4 victory over Evgeniya Rodina, who had routed Eugenie Bouchard in the first round.

Pliskova and Svitolina were two of the eight players who arrived at the U.S. Open with a chance to be ranked No. 1 after the tournament, and three of them already have lost. No. 2 Simona Halep was ousted by Maria Sharapova on the opening night of the tournament, while No. 5 Caroline Wozniacki, No. 6 Angelique Kerber — the defending champion — and No. 7 Johanna Konta also lost.

Pliskova, the runner-up here last year, will have to get back to the final to remain atop the rankings, or win the tournament if third-seeded Garbine Muguruza loses in the semifinals.

Nadal has returned to No. 1 on the men’s side, though Federer has a chance to reclaim that spot.

Both players are in second-round action Thursday, with Federer looking for his 80th U.S. Open victory.

A number of players were on the court for a second straight day after almost all of Tuesday’s action was postponed by rain.

Federer and Nadal did get their matches in that day under the roof at Arthur Ashe Stadium, so they both had Wednesday off. Federer used his time to practice at Central Park .

The five-time U.S. Open champion faced Mikhail Youzhny of Russia in an afternoon match. An 80th victory would break a tie with Andre Agassi and leave Federer behind only Jimmy Connors’ 98 victories at the U.S. Open.

Youzhny was a semifinalist at Flushing Meadows in 2006 and 2010, but he’s 0-16 lifetime against Federer.

The top-ranked Nadal faces Japan’s Taro Daniel in the second night match at Ashe.

No. 24 Juan Martin del Potro, another former U.S. Open champion, swept past Spanish qualifier Adrian Menendez-Maceiras 6-2, 6-3, 7-6 (3), but No. 15 Tomas Berdych was beaten by Ukraine’s Alexandr Dolgopolov, 3-6, 6-1, 7-6 (5), 6-2.

French Open champion Jelena Ostapenko also advanced, but No. 23 Barbora Strycova was routed 6-1, 6-1 by American Jennifer Brady. Japan’s Naomi Osaka, who upset Kerber in the first round, also advanced to the third round.