By Frank Pingue

The former world number one, playing in just her fourth tournament since returning from an 11-month layoff in June, capped the victory in style with an ace and then raised her arms in the air before jumping up and down repeatedly.

Williams, who won the Stanford Classic last month, held her serve throughout the 77-minute match and called her game solid despite acknowledging there is room for improvement for the U.S. Open, which begins on August 29.

"My game is here and I feel like there are a lot of improvements I want to make -- being able to close out big points and winning on big points and capitalizing on that and still returning a little bit better," Williams told reporters.

"But overall it's solid, I want to definitely keep it up and not go down."

Stosur went toe-to-toe with Williams in a first set that went with serve until the 13-times grand slam champion broke in the ninth game with a forehand volley to the empty side of the court. She served out in the next game.

Williams had sent a screaming backhand winner down the line one point previously, which she said was when the match turned in her favor.

"I definitely think that's when the match started changing, but for the most part I was really fighting until that point," Williams said.

Williams broke Stosur in the opening game of the second set with a cross-court winner.

The 10th-seeded Stosur held serve in the next game but tournament organizers, perhaps unknowingly, showed little faith in her ability to mount a comeback.

During a change of sides before Williams had her first chance to serve for the match, they squeezed in a short clip on the main scoreboard thanking fans for attending the tournament and asking them to buy tickets for next year.

Williams followed that with a solid final game, firing four of her nine aces past a helpless Stosur, who saw only one break point during the match.

"For me to be able to win I had to play close to my best tennis, and I wasn't quite at that that mark," Stosur told reporters. "She makes it look very easy and it's not that easy just to come back on tour and win two events in your first four tournaments."

She entered the tournament as the world number 80 but is projected to go as high as 31 when the rankings are released on Monday.

Despite that, Williams considers herself an underdog for the year's final grand slam. "I never go in as a favorite, I feel like I'm still the underdog," she said.

"I went through a lot of things physically, mentally and emotionally, and going through so much so I am just taking it one day at a time and kind of like one match at a time."

Victoria Azarenka withdrew from the doubles final with an injured right hand, clouding the world number four's participation in the U.S. Open.

Azarenka, who lost in straight sets to Williams in Saturday's semi-final, withdrew from the doubles match along with playing partner Maria Kirilenko before taking the court.

(Editing by Stephen Wood)