Serena Williams after her win, in Stanford, on Sunday. (AFP)

Stanford: Serena Williams sounded an ominous warning to her rivals that she will be a genuine contender at the U.S. Open after winning the Stanford Classic on Sunday in her third tournament back from injury.

Williams overpowered third seed Marion Bartoli of France 7-5, 6-1 in final and her opponent, who triumphed when they last met in the fourth round at Wimbledon this year, applauded the American’s performance.

American Williams came from 2-4 down in the opening set and then dominated the rest of the match with booming serves and hard groundstrokes to claim her first title since Wimbledon last year.

The 13-times Grand Slam champion, who returned to the Tour in June after taking almost a year off due to injury and illness, triumphed for the first time on home soil since her victory at the 2008 U.S Open.

“I haven’t won a tournament in forever that wasn’t a Grand Slam so it’s cool,” said Williams, whose last non-major title was the 2009 WTA Championships in Doha.

“I put a lot of work into this week. I want to take this whole (hardcourt) swing serious. It’s a good time for me.”

Bartoli used her vicious groundstrokes to lead 4-2 in the first set but then suffered an injury to her right hand and her game deteriorated as she could not grip her racket properly for her serve and forehand.

She served for the set at 5-4 but was broken when she hit a forehand long. Williams then held and again broke the Frenchwoman to win the set when her opponent erred on a backhand.

“I knew before the match that it would be different from Wimbledon,” said Bartoli, who suffered a bone bruise on her hand.

“I managed to play well until my hand was disturbed, but that doesn’t take anything away from Serena who played really well.”

Williams won five consecutive games to take command of the second set before ending the match with a rasping forehand crosscourt winner followed by a 113mph service winner.

“I never lose hope in my serve,” said Williams, who unleashed 11 aces in the match. “Sometimes it doesn’t show up, but I keep hitting it.

“I have an opportunity to be healthy and be here that I’m so grateful,” added the American, who is next scheduled to play in the WTA event in Toronto starting on August 8.