Number one seed Madison Keys stunningly lost in the second round, while Venus Williams was also ousted at the Volvo Car Open.
Keys faded against fellow American Shelby Rogers, who rallied to a 4-6 6-1 6-1 win before bad weather suspended play in Charleston on Wednesday.
A finalist at the event in 2015, Keys trailed 3-0 in the opening set before recovering to take the lead in the match.
However, Rogers hit back and won 11 consecutive games to book her spot in the last 16.
Next up is Japanese teenager Naomi Osaka, who eliminated 13th seed Zhang Shuai 6-4 6-4.
American third seed Williams departed the WTA Premier tournament after going down to Laura Siegemund in three sets, despite having two match points in the third.
Williams had reached the semi-finals at the Miami Open and quarter-finals of the BNP Paribas Open, but the seven-time grand-slam champion was outlasted by Siegemund 6-4 6-7 (3-7) 7-5.
Awaiting Siegemund in the round of 16 is Lucie Safarova after the 15th seed beat Bethanie Mattek-Sands 6-3 6-3.
Olympic champion Monica Puig said goodbye to Charleston, defeated 6-0 6-7 (3-7) 6-2 by Daria Kasatkina, while fourth seed Elena Vesnina was a 7-6 (9-7) 7-6 (7-3) loser against Fanny Stollar.
Elsewhere, Dutch seventh seed Kiki Bertens saw off Kateryna Bondarenko 6-2 7-5, eighth seed Anastasija Sevastova overcame Andrea Petkovic 6-3 6-4, Irina-Camelia Begu - the 10th seed - prevailed 4-6 6-2 7-6 (8-6) against Kristina Kucova and 11th seed Mirjana Lucic-Baroni was a 6-3 6-2 winner against Mona Barthel.
Meanwhile, the second-round clash between Caroline Wozniacki and Annika Beck was postponed due to heavy rain and lightning.