Unseeded Sloane Stephens, 28, beat Australia’s Ajla Tomljanovic 6-3, 6-4, while 14th-seeded Coco Gauff, 17, topped fellow American Lauren Davis 6-2, 7-6 (2).
Gauff is one win from matching her best result of the year, a semifinal finish at Adelaide, Australia. Stephens, who won the Charleston championship five years ago, had just one singles match victory on the year before this week.
In other third-round action, Montenegro’s Danka Kovinic upset third-seeded Petra Kvitova of the Czech Republic 6-4, 6-1; 12th-seeded Ons Jabeur of Tunisia defeated France’s Alize Cornet 6-3, 6-3; and 15th-seeded Veronika Kudermetova of Russia routed Japan’s Kurumi Nara 6-0, 6-3.
Spain’s Paula Badosa beat American Caty McNally 6-3, 6-3, and Kazakhstan’s Yulia Putintseva advanced when sixth-seeded Spaniard Garbine Muguruza retired despite leading 6-0, 2-2. Muguruza had to stop her match due to a left leg injury.
Top-seeded Ashleigh Barty of Australia won the final match of the evening, edging the United States’ Shelby Rogers 7-6 (3), 4-6, 6-4.
Maria Camila Osorio Serrano, a 19-year-old Colombian who received a wild-card entry into the event, advanced to the quarterfinals in Bogota, Colombia, with a 6-3, 6-3 win over seventh-seeded Tereza Martincova of the Czech Republic.
Osorio Serrano, ranked 180th in the world, will oppose Switzerland’s Stefanie Voegele in a quarterfinal match on Friday.
The second round concluded with two other matches. Fifth-seeded Tamara Zidansek of Slovenia ousted Italy’s Giulia Gatto-Monticone 6-2, 6-3, and France’s Harmony Tan got past Chile’s Daniela Seguel 6-4, 7-6 (3).