The scores were 6-0, 4-6, 6-4, making it the second day in a row that Wozniacki played a three-set match. On Friday, the Dane topped sixth-seeded Aleksandra Wozniak of Canada 6-2, 6-7 (1-7), 6-2.
"I tried to do what I wanted to do and not let anything frustrate me," Stosur said.
Saturday's other semifinal winner, fourth-seeded Francesca Schiavone of Italy, clobbered India's Sania Mirza 6-2 6-1. Mirza lost in less than an hour, with Schiavone recording a 4-0 advantage in service breaks.
"I served well and was aggressive right to the end," Schiavone said.
Sunday's Stosur-Schiavone winner collects a $37,000 champion's check.
Stosur has a 3-1 advantage lifetime in head-to-head matches with Schiavone.
2014: The Year in Music [PHOTOS]