Venus Williams scored a second-round victory in the WTA Family Circle Cup, a day after sister Serena crashed out of the claycourt tournament.

Venus, the 11th seed who won the title on the green clay at Charleston in 2004, fought hard to defeat South African Chanelle Scheepers 7-5 7-5.

“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,” said Venus, who lost in the semi-finals last year to her younger sister Serena.

Serena, the world No.1 and top seed, was stunned on Tuesday by Slovakian Jana Cepelova, the American unable to maintain her momentum after lifting an emotional seventh title in Miami at the weekend.

Venus said the defeat would give her sister a well-deserved chance to rest. Venus, herself a seven-time grand slam champion who has battled injury and illness the past two years, is very much alive.

She won her first WTA title in 16 months in Dubai in February.

“I’ve been playing well from behind lately, which is something you really have to be able to do to win big matches,” she said.

“You’re not always going to be ahead.”

She next faces rising Canadian star Eugenie Bouchard, the sixth seed.

Another up-and-coming youngster, Ukraine’s Elina Svitolina, upset fifth-seeded American Sloane Stephens 6-4 6-4 to book a third-round berth.

Svitolina next faces another teenager in 17-year-old Belinda Bencic of Switzerland, a 6-2 6-1 winner over New Zealand’s Marina Erakovic.

Second-seeded Serbian Jelena Jankovic, the 2007 champion, reached the third-round with a convincing 6-0 6-3 victory over American Lauren Davis.

Third-seeded Italian Sara Errani eased through, winning the first set against Kiki Bertens 6-3 before the Dutch player retired.

Fourth-seeded German Sabine Lisicki, who won the title in 2009, had to work harder, but booked a third-round berth with a 7-5 4-6 6-3 victory over American Vania King.