The opening set proved to be a difficult one for Stosur, who struggled to hold any of her service games. She eventually managed to record just one game as Azarenka eased into the lead with a 6-1 success.
However, Australia's Stosur responded well during the second set. Both players found it hard to find any consistency while serving, but it was Stosur who eventually came out on top 6-4.
The deciding set was similar to the first two and at one point four service games in succession resulted in breaks.
With very little to separate the pair, the set headed into a tie-breaker.
Azarenka began the breaker brightly and soon found herself 4-0 in front. Back came Stosur though as the world number seven won five of the next six points to level up at 5-5.
Stosur was then broken again, before Azarenka served out to book her place in the semi-finals.