CHARLESTON, S.C. — Serena Williams overcame a slow start today to advance to the finals of the Family Circle Cup by defeating unseeded Alize Cornet of France 7-5, 6-3.

Williams, ranked ninth in the world and seeded fifth this week, is looking for her third tournament title of 2008. She will face either fourth-seeded Elena Dementieva or ninth-seeded Vera Zvonareva in the Sunday final of the $1.3 million tournament.

Williams trailed 4-1 in the first set, but fought back, breaking Cornet twice at love before taking the set. In a second set featuring long baseline rallies, Williams broke Cornet in the eighth game, then held serve at love to take the match.

"In just the whole match I thought she played really well, and I just wasn't playing my game," Williams said. "I got caught a little bit on the defensive a lot and I wasn't doing anything I should have been doing."

Cornet, an 18-year-old ranked No. 40 in the world, also made the semifinals at Amelia Island last week. She was runner-up earlier this year at Acapulco, her best showing on the tour since joining it last year.

Saturday was the first time she faced Williams, who was guaranteed of surpassing $19 million in earnings with the victory.

"It was a little bit of a surprise for her because she didn't know me," Cornet said. "I was like making the pressure on her and it was working and after 4-1, you know, she played better."

Cornet said she has learned a lesson by reaching two consecutive semifinals. "I have to fight and I have to play my game, and I think I have the level now for beating the best, so it's a lot of confidence for me," she said.

Williams said she will surely be facing Cornet again.

"She gets a lot of balls back, and those kind of players are usually around for a good 20 years," Williams said.