Serena Williams of the US reacts while holding the singles championship trophy after defeating France's Marion Bartoli in their Stanford Classic final tennis match in Stanford, California, July 31, 2011. [Photo/Agencies]

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

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

"She has really improved her level from Wimbledon," the ninth-ranked Bartoli told reporters. "She beat (Maria) Sharapova and (Sabine) Lisicki easily, and everything is just better -- her serve, her movement.

"I would pick Serena (as the US Open favorite) considering how many times she won there. Six weeks from now, she'll be more than 10 percent better."

In winning five matches on her way to the Stanford title, Williams experienced only one hiccup when she dropped a set to Russian Maria Kirilenko in the second round.

The American crushed Australian Anastasia Rodionova 6-0 6-0 in the first round, eased past fifth-ranked Sharapova 6-1 6-3 in the last eight and destroyed Wimbledon semi-finalist Lisicki 6-1 6-2 in the semi-finals.

US Fed Cup captain Mary Joe Fernandez was hugely impressed by how Williams "managed" her matches.

"Even when she was at the top of her game, she would go off once in a while and in her last three matches I didn't see that," Fernandez told Reuters.

"She wasn't blasting players off the court and she worked the points. She wasn't hitting winners left and right and she still has a lot of room to improve. At Wimbledon, she was not as sure with her reactions, plus she looked fitter."

Former world number one Williams, who returned to the tour in June after taking almost a year off due to injury and illness, is projected to break into the top 80 when the new rankings are issued on Monday.

While she has completed impressive comebacks from knee injuries in the past, she felt her own reaction to this most recent return from a severe foot injury and pulmonary embolism was unique.

"The hunger is a lot but it's different," Williams said. "It is more happiness and I feel relief and grateful."

Williams, who was ranked a lowly 169th coming into the Stanford Classic, plans to take a week's break before returning to competition in Toronto and Cincinnati.

She believes she is still well short of her best while acknowledging she has seen plenty of positive improvement.

"I just put myself at the bottom (rung) because I want to keep it going, but my confidence is better and that is what I was praying for," she said.

The US Open, where Serena Williams has won the singles title three times, takes place from Aug. 29-Sept. 11.