World number five Samantha Stosur won her second-round match at the WTA event in Charleston, South Carolina.
Stosur, the 2010 champion, was too strong for American qualifier Jamie Hampton, winning 6-0, 7-5.
Fellow Australian Anastasia Rodionova also stayed alive in the tournament with a 7-5, 6-3 defeat of Spain's Anabel Medina Garrigues.
"I'm really looking forward to this part of the season. I hope I can have a good week here," Stosur said.
"Today I lost serve for the first time when I was serving for the match, but she played some good points.
"She probably felt she had nothing to lose and went for it more. But from 5-all I played two good games."
Meanwhile, Serena and Venus Williams made a successful transition to clay, easing through their opening matches with straight-set victories.
Fifth-seed Serena, the 2008 Charleston champion, hammered 11 aces in overpowering last year's runner-up Elena Vesnina, 6-3, 6-4, in a second-round match.
World number 87 Venus, who returned to the tour last month in Miami after being out for seven months due to illness, needed just 79 minutes to dispatch qualifier Iveta Benesova of the Czech Republic, 6-4, 6-3, in a first-round encounter.
"Miami was definitely a whirlwind," Venus said Tuesday.
"A lot of times I ended up the victor at the end of these matches and I didn't really know how it happened."
ABC/ReutersTags: tennis, sport, united-states First posted April 04, 2012 12:54:17