Two-time Grand Slam champion Petra Kvitova overcame an early setback to beat Kateryna Kozlova and reach the US Open third round.
The Czech sixth seed came back from a break down in the first set and saved a set point to beat the Ukrainian 7-6 (7-3) 6-2.
But Kvitova's compatriot Marketa Vondrousova, the 12th seed, became the highest-ranked woman to make an exit.
The 2019 French Open runner-up lost 6-1 6-2 to Belarus' Aliaksandra Sasnovich.
Former champion Angelique Kerber came through a tough encounter with fellow German Anna-Lena Friedsam, winning 6-3 7-6 (8-6), while there were also victories for Croatian eighth seed Petra Martic and Estonian 14th seed Anett Kontaveit.
Top seed Karolina Pliskova is in action later on Wednesday when she faces a tricky test against former world number four Caroline Garcia of France, while Japanese fourth seed and 2018 champion Naomi Osaka takes on Italy's Camila Giorgi.
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