Beatriz Haddad Maia (23), then Karolina Muchova (14), were knocked out on Tuesday, following Emma Navarro (9) the day before, but the elite were otherwise unscathed.
Two Americans were the victors, Hailey Baptiste and Alycia Parks.
Baptiste, who is currently ranked a career-high 70th, accounted for Brazilian Haddad Maia 4-6 6-3 6-1.
With Navarro losing on Monday to Jessica Bouzas Maneiro in the same segment of the draw, the opportunity has opened up for an unseeded player to advance to the fourth round.
Nao Hibino, of Japan, who now plays Baptiste, and American Robin Montgomery, who meets Bouzas Maneiro, are the others in the quartet.
Whoever emerges into the last 16 could then meet former French Open runner-up Sofia Kenin. She eased past Frenchwoman Varvara Gracheva 6-3 6-1 and now plays two-time Australian Open champion Victoria Azarenka.
Late in the evening on Court Simonne Mathieu Parks became the last player into the second round when she beat Czech Muchova 6-3 2-6 6-1.
The powerful Parks, ranked 52, hit 36 winners and nine aces, winning the last five games on the spin.
Two higher ranked Americans who progressed earlier were second and third seeds Coco Gauff and Jessica Pegula, past Australia's Olivia Gadecki 6-2 6-2 and Romanian Anca Todoni 6-2 6-4, respectively.
Polish 25th seed Magdalena Frech defeated Tunisia's former Wimbledon and US Open runner-up Ons Jabeur 7-6 (7-4) 6-0 while Russian sixth seed Mirra Andreeva eased past Spain's Cristina Bucsa 6-4 6-3.
with agencies
