American third seed Shelby Rogers eased past qualifier Claire Liu 6-2 6-2 on Wednesday.
Ons Jabeur – who reached the semi-finals of the Volvo Car Open – made a winning start at the WTA 250 event after topping Stefanie Vogele.
Shelby Rogers defeated Caty McNally while fifth seed Misaki Doi retired in the third set tiebreaker on the first day in Charleston.
Veronika Kudermetova and Maria Camila Osorio Serrano landed maiden WTA titles on Sunday, completing stellar weeks in their young careers.
Veronika Kudermetova took care of Paula Badosa, and her reward is Danka Kovinic in the Charleston Open final.
World number one Ash Barty's eight-match winning run was ended by 71st-ranked Paula Badosa in Charleston.
World number one Ashleigh Barty won over Shelby Rogers but top 10 seeds Petra Kvitova and Garbine Muguruza both bowed out on Thursday.
With France in a nationwide lockdown, the decision has been taken to shift the start of the French Open to May 30.
Sofia Kenin, Belinda Bencic and Elise Mertens were all beaten at the Volvo Car Open, where Ash Barty moved through.
Two-time grand slam champion and sixth seed Garbine Muguruza dispatched qualifier Magdalena Frech 6-1 6-3 on Tuesday.