Upset losses for a host of seeds haven't done anything to help the cause of Daria Gavrilova and Samantha Stosur, after the Australian pair won through to the third round of the WTA event in South Carolina.
Gavrilova celebrated her selection for what would be a Fed Cup debut with a comfortable 6-4 6-0 win over China's Zhang Shuai, while Stosur beat Slovakian Jana Cepelova 6-4 7-5 in an hour and 35 minutes.
World No.37 Gavrilova will take on Sloane Stephens for a quarter-final berth after the American seventh-seed beat Danka Kovinic 6-4 6-3.
After coughing up 11 double faults in scraping through the first round, Stosur looked slightly better in setting up a third-round meeting with Italian fifth-seed Sara Errani, who dominated Kazakhstan's Yaroslava Shvedova 6-0 6-3.
Errani and Stephens both avoided the carnage that resulted in No.2 Belinda Bencic, No.4 Lucie Safarova, No.6 Andrea Petkovic and No.8 Madison Keys all losing in the second round.
Bencic was beaten by Russian qualifier Elena Vesnina 6-1 6-1, Safarova fell to American wildcard Louisa Chirico 6-3 6-3, 2014 champion Petkovic lost to Monica Puig 7-5 6-2 while Keys fell to Germany's Laura Siegemund 6-7 (3-7) 6-4 6-4.
Chasing her 50th WTA title, Venus Williams cruised past fellow American Alison Riske 6-4 6-2.
"I think today, I was aggressive, which is important for my game, even on clay," third-seeded Williams said.
"You still want to dictate the points."
Top seed and defending champion Angelique Kerber needed a third-set tiebreaker to escape her opening match over Lara Arruabarrena.
Eugenie Bouchard withdrew from her match with Lourdes Dominguez Lino with an injury to her lower abdomen when trailing 6-4 1-6 1-0.
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