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New York - Karolina Pliskova had to battle back from a set down to make the US Open last 32 on Thursday and hang on to her world number one spot.
The Czech player, who was runner-up in 2016, downed American qualifier Nicole Gibbs 2-6, 6-3, 6-4.
She was joined in the third round by fourth seed Elina Svitolina, one of the pretenders to her top ranking, and French Open champion Jelena Ostapenko.
"It's easier for the other girls to play me as there is more pressure being number one," said Pliskova, who faces either Chinese 27th seed Zhang Shuai or Risa Ozaki of Japan for a place in the last 16.
"Everyone plays their best tennis against me and I felt that today," added Pliskova, who would have lost the number one spot she has held for just six weeks had she lost.
Gibbs, ranked 127 in the world, had only won three matches on tour this year before the US Open, but she raced to a 5-1 lead on her way to pocketing the first set.
Pliskova eventually overpowered the 24-year-old Californian, breaking in the eighth game of the second set and seventh in the decider.
Later Thursday, Roger Federer, chasing a record sixth US Open and third major of the year, faces two-time semi-finalist Mikhail Youzhny, boasting a perfect 16-0 record against the former world number eight.
Federer, with a 20th Grand Slam title in his sights, needed five sets to get past US teenager Frances Tiafoe in his opening match on Tuesday.
Victory over the 35-year-old Youzhny would give him his 80th win at the tournament.
Top seed Nadal, the 2010 and 2013 champion, faces Japan's Taro Daniel, the New York-born world number 121.
After the success of Canadian 18-year-old Denis Shapovalov, fellow "NextGen" stars Andrey Rublev and Taylor Fritz also look to upset the odds and make the third round.
Rublev, 19, tackles seventh-seeded Grigor Dimitrov of Bulgaria while Fritz, also 19, faces Dominic Thiem, the sixth seed.
Ukraine fourth seed Svitolina reached the last 32 for a third successive year by breezing past Russia's Evgeniya Rodina 6-4, 6-4.
Roland Garros champion Ostapenko, the 12th-seeded Latvian, made the third round for the first time with a 6-4, 6-4 win against Romania's Sorana Cirstea.
At the start of the day's play, four of the top 10 women seeds had been knocked out - Simona Halep, Caroline Wozniacki, defending champion Angelique Kerber and Johanna Konta.
One to survive was Svetlana Kuznetsova, the eighth-seeded 2004 champion.
She faces Japan's Kurumi Nara having saved three match points in her opener against Marketa Vondrousova.
Results from day 4 of the US Open on Thursday (x denotes seeding):
Men
Second round
Viktor Troicki (SRB) bt Stefano Travaglia (ITA) 7-6 (8/6), 7-5, 6-0
Aleksandr Dolgopolov (UKR) bt Tomas Berdych (CZE x15) 3-6, 6-1, 7-6 (7/5), 6-2
Damir Džumhur (BIH) bt Cedrik-Marcel Stebe (GER) 4-6, 6-4, 6-0, 6-1
John Millman (AUS) bt Malek Jaziri (TUN) 6-1, 7-6 (7/1), 6-1
Women
Second round
Karolína Plíšková (CZE x1) bt Nicole Gibbs (USA) 2-6, 6-3, 6-4
Jennifer Brady (USA) bt Barbora Strycová (CZE) 6-1, 6-1
Monica Niculescu (ROM) bt Ana Bogdan (ROM) 6-2, 3-6, 6-3
Elina Svitolina (UKR x4) bt Evgeniya Rodina (RUS) 6-4, 6-4
Jelena Ostapenko (LAT x12) bt Sorana Cirstea (ROM) 6-4, 6-4
Darya Kasatkina (RUS) bt Christina McHale (USA) 7-5, 6-3
Kaia Kanepi (EST) bt Yanina Wickmayer (BEL) 6-4, 6-2
Naomi Osaka (JPN) bt Denisa Allertová (CZE) 6-3, 4-6, 7-5
