Top seed Ons Jabeur advanced to the last 16 at the MUSC Health Women's Open, while Magda Linette was a casualty on Tuesday.
Jabeur – who reached the semi-finals of the Volvo Car Open – made a winning start at the WTA 250 event after toppling Stefanie Vogele 6-4 6-1.
The Tunisian won 88.9 per cent of her first serves to set up a clash with qualifier Alycia Parks – the latter eased past fellow American Grace Min 6-1 6-4.
However, second seed Linette crashed out at the hands of in-form Colombian Maria Camila Osorio Serrano.
Osorio Serrano, who claimed her maiden singles title at the Copa Colsanitas in Bogota last week, upstaged Linette 6-3 4-6 7-5.
Elsewhere, 15-year-old wildcard Linda Fruhvirtova – in just her second WTA main-draw appearance – progressed 6-2 6-7 (7-9) 4-4 after fourth seed Alize Cornet retired in the final set.