The Australian lost the opening set in convincing fashion, having been broken three times.
But the world number nine, who missed out on a place in the WTA Championships last week, took advantage of two of her five break points to level the match.
And the 2011 US Open champion took the match in 115 minutes with the solitary break in the deciding set.
Stosur, who won the first of her three WTA titles in Osaka in 2009, now meets Jamie Hampton of the USA.
Other Results:
Misaki Doi (Japan) beat Olga Puchkova (Russia) 6-3 6-2
Jamie Hampton (U.S.) beat Tamarine Tanasugarn (Thailand) 7-5 7-5
Chang Kai-Chen (Taiwan) beat Casey Dellacqua (Australia) 7-6(4) 6-3
