Fourth seed and former champion Angelique Kerber overcame a second-set wobble against Sweden’s Johanna Larsson to make the US Open last 32.
The German, who had never lost a set in three previous matches with Larsson, eventually won 6-2 5-7 6-4.
Angelique Kerber plays Dominika Cibulkova next after the Slovak advanced despite a two-point deduction for returning late from a heat break.
Fifth seed Petra Kvitova got past China’s Wang Yafan 7-5 6-3.
Kvitova, 28, broke late to seal the opening set after initially letting a 4-1 lead slip and Wang’s consistent groundstrokes and a solid serve kept the world number 90 in touch in the second set in a stubborn display.
Temperatures at Flushing Meadows were once again high enough for organisers to apply their extreme heat policy, but Cibulkova was deemed to have taken longer than the permitted 10 minutes to cool down between the second and third sets in her match against Taiwan’s Hsieh Su-wei.
“[The umpire] told me I was one minute late. I’m getting two points’ penalty. You cannot be serious,” said Cibulkova, who won 7-6 (7-3) 4-6 6-4.
“It took me, I think, more than three minutes walking through the people, because there were so many fans and so many people. I couldn’t believe it.”
American Madison Keys, who lost last year’s final to Sloane Stephens, beat compatriot Bernarda Pera 6-4 6-1.
Kvitova next plays 20-year-old Belarusian Aryna Sabalenka, who won the New Haven title earlier in August.
Sabalenka beat 2010 runner-up Vera Zvonareva 6-3 7-6 (9-7) to make the last 32.
She is joined by her compatriot Aliaksandra Sasnovich who upset Russia’s in-form 11th-seed Daria Kasatkina 6-2 7-6 (7-3)
Sasnovich will face Naomi Osaka – who clinched her biggest career title at Indian Wells in March – after the Japanese beat Julia Glushko 6-2 6-0.