Ajla Tomljanovic was the lone Australian to progress to the second round of the WTA green-clay tournament in South Carolina.
The 14th-seeded Tomljanovic cruised in the first set of her opening match but was pushed to a tiebreaker before she accounted for Polish world No.85 Magda Linette 6-2, 7-6 (9-7).
Tomljanovic will face Slovenian world No.64 Tamara Zidansek in the round of 32.
Melbourne's Destanee Aiava was outclassed by ninth-seeded Belinda Bencic in their first-round encounter, the Swiss steamrolling her way past the teenage qualifier in less than an hour, 6-3, 6-0.