Stosur, the No. 3 seed, posted a 7-5, 6-1 win over fourth-seeded Francesca Schiavone of Italy.
"I'm very, very pleased to win my first title after losing five previous finals," Stosur said. "My next goal is to reach the Top 10 for which I would need to play like today every day."
Stosur, who is 4-1 in matches against Schiavone, has been on 22 winning doubles teams on the tour. She is 1-10 in singles finals.
"There were just a few points difference in the first set," Schiavone said. "It was very close. She took her chances and she deserved to win. I gave her nothing for free; she won every point."