Caroline Wozniacki and Angelique Kerber eased through at the U.S. Open as Agnieszka Radwanska exited on Wednesday.
Top-10 seeds Simona Halep, Maria Sharapova and Jelena Jankovic also advanced on a warm day at Flushing Meadows.
Wozniacki, considered an outside chance of claiming her maiden grand slam title, brushed past Belarusian Aliaksandra Sasnovich 6-3, 6-4 in their second-round clash.
The Danish 10th seed had few problems as Sasnovich produced 34 unforced errors.
Hard-hitting left-hander Kerber was also untroubled as the German sixth seed crushed Russia's Alla Kudryavtseva 6-2, 6-4.
Romanian world number two Halep needed less than an hour to thrash Slovak Jana Cepelova 6-2, 6-1.
Sharapova, the Russian fifth seed, never hit her best form but was still capable of getting past Romania's Alexandra Dulgheru 4-6, 6-3, 6-2.
In an enticing third-round clash, Sharapova will face Sabine Lisicki after the German 26th seed beat American Madison Brengle 6-4, 6-1.
Serbian ninth seed Jankovic was too good for Bulgarian Tsvetana Pironkova, claiming a 7-5, 6-4 victory.
The day's biggest surprise was Radwanska's loss as the Pole's poor record at the Open continued.
China's Peng Shuai was a convincing 6-3, 6-4 victor over the fourth seed, who has never progressed beyond the fourth round at the final grand slam of the year.
Talented American Sloane Stephens was another shock loser, beaten 5-7, 6-4, 6-2 by Swede Johanna Larsson.
It continued what has been a disappointing 2014 for the 21st-seeded Stephens, who has been unable to build on her good showings at majors last year.
Italian 13th seed Sara Errani overcame Australian Anastasia Rodionova 6-4, 7-6 (7-2) and Swiss teenager Belinda Bencic was too good for Japanese 31st seed Kurumi Nara 6-4, 4-6, 6-1.
American veteran and 19th seed Venus Williams crushed Swiss Timea Bacsinszky 6-1, 6-4 and French 22nd seed Alize Cornet beat Slovak Daniela Hantuchova 6-3, 6-3.
Andrea Petkovic, the German 18th seed, battled to a 3-6, 6-3, 7-6 (7-5) win over Puerto Rico's Monica Puig in an entertaining encounter.
Czech 14th seed Lucie Safarova claimed a 6-3, 4-6, 6-2 win over China's Zheng Saisai, Croatian Mirjana Lucic-Baroni beat Israel's Shahar Peer 6-7 (6-8), 6-3, 6-2 and Italian 28th seed Roberta Vinci did enough to get past Romanian Irina-Camelia Begu 2-6, 6-4, 6-1.