It was another long day for Williams, ranked No. 28 in the world, who needed 1 hour, 50 minutes to finish the straight-set victory over the South African. Williams fell behind 3-1 in the first set and trailed 4-1 in the second.
"She was playing so well, but the good thing is that when I get behind, I give even more effort and get even more focused. And I've been playing well from behind lately, which is something you really have to be able to do to win big matches," Williams said.
The seven-time Grand Slam champion has battled injuries and Sjogren's syndrome, a fatigue-causing autoimmune disease, during the past two years. She was on the green clay in Charleston for 2 hours, 15 minutes on Tuesday in a three-set victory and said she has been ill this week.
"I'm still dealing with the bug, but my goal is just to hang in there until it hopefully goes away and then I can just continue to play my way into the tournament and play stronger," she said. "But it's definitely a challenge."
On Tuesday night her sister, top-ranked Serena Williams, was stunned 6-4, 6-4 by Jana Cepelova of Slovakia, ranked No. 78 in the world, in the second round. Serena Williams said later she was tired and needed time off to regroup.
"I definitely can see where she is tired and her body is taxed," Venus Williams said of her sister. "She gave an amazing effort yesterday, and she's going to get some well-deserved time off from winning."
Venus Williams, who won the Family Circle a decade ago, now faces No. 20 Eugenie Bouchard.
No. 8 Jelena Jankovic, the tournament's No. 2 seed, later scored a 6-0, 6-3 victory over American Lauren Davis. Jankovic won the Family Circle back in 2007 and was runner-up last year to Serena Williams.
Earlier Wednesday, American Sloane Stephens was upset 6-4, 6-4 by 19-year-old Elina Svitolina of the Ukraine, who has a career-high No. 35 ranking. It was her fourth career victory over a top 20 player, the third coming last week at the Sony Open.
"She played pretty well, and it's just unfortunate that I lost, but I mean, you can just learn from the mistakes and things like that and build on it," Stephens said.
"I started to believe more in myself that I can compete with players like this, top level, top 20 and top 10," said Svitolina, who is making her first appearance on the green clay in Charleston. "I think this is the key. That I believe more in myself and I play more solid from the baseline and trying to go forward to finish the point earlier."
Italian Sara Errani, ranked No. 11 in the world and seeded third, advanced as well. She won the first set 6-3 when qualifier Kiki Bertens of the Netherlands retired. Fourth-seeded Sabine Lisicki of Germany was extended to three sets before defeating American Vania King 7-5, 4-6, 6-3.
Andrea Petkovic of Germany, the 14th seed, defeated Lourdes Dominguez Lino of Spain 6-0, 6-0 while Shuai Peng of China eliminated 15th-seeded Madison Keys of the United States 6-1, 6-7 (3) and 7-6 (4). Qualifier Belinda Bencic of Switzerland defeated Marina Erakovic of New Zealand 6-2, 6-1.