The fifth-seeded Stosur needed 1 hour, 28 minutes to beat the American after struggling through the opening set.
Stosur, ranked 13th, was granted a wild card after losing to Olga Govortsova last week in the opening round of the Bank of the West Classic. She wanted to get more time on the hard courts in preparation for the US Open, which she won in 2011.
Francesca Schiavone, the 2010 French Open champion, defeated her Italian countrywoman, Flavia Pennetta, 7-6 (4), 6-7 (6), 6-4 in a first-round match that lasted 2:58.
No 6 seeded Jelena Jankovic of Serbia faced American Mallory Burdette in a night match.