Samantha Stosur, the last woman to beat Serena Williams at the US Open four years ago, and two-time runner-up Victoria Azarenka made the third round Thursday.
Australian 22nd seed Stosur breezed past Russia's Evgeniya Rodina -- one of two mothers to have reached the second round -- 6-1, 6-1.
Stosur, 31, fired eight aces with no double faults and hit 29 winners in her quickfire win, which gave her a third-round encounter against Italian 16th seed Sara Errani.
Despite the victory, Stosur hit out at organisers, who she claims have blundered over transport for players as well as practice court arrangements.
Stosur said she was forced to switch courts on Wednesday when Serena Williams needed a place to practice.
"She kicked me off my practice court. A few issues," said the Australian.
Azarenka, seeded at 20, made the finals in 2012 and 2013, losing to Williams in three sets on both occasions.
The Belarusian, playing in just her 13th tournament of an injury-hit season, saw off 2009 semi-finalist Yanina Wickmayer of Belgium, 7-5, 6-4.
"She doesn't give you much time. She came out firing and I had to fight and dig deep," said the 26-year-old.
Errani made the next stage by seeing off Latvian qualifier Jelena Ostapenko 0-6, 6-4, 6-3 with German 18th seed Andrea Petkovic defeating Russia's Elena Vesnina 6-3, 7-6 (7/4).
Also in action Thursday is Swiss fifth seed and French Open champion Stan Wawrinka, who faces South Korean teenager Hyeon Chung.
In the women's draw, second seed Simona Halep faces Ukraine qualifier Kateryna Bondarenko, who is playing the US Open for the first time since 2012 after taking time out to have her first baby.
Fourth-seeded Caroline Wozniacki, the 2009 and 2014 runner-up, plays Petra Cetkovska of the Czech Republic.
Two-time Wimbledon winner Petra Kvitova, the fifth seed, takes on Nicole Gibbs of the United States.
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