Azarenka, who won on her 21st birthday, will play for the title on Sunday against the winner of a later semi-final between Polish third seed Agnieszka Radwanska and Russian fifth seed Maria Sharapova.
"I'm happy with the way I played," Azarenka said. "I'm finally injury-free and I'm enjoying my time on the court.
Azarenka, who still seeks her first title of the season, is 1-2 lifetime against Sharapova and 4-2 overall against Radwanska.
Stosur, in her sixth semi-final of the year, leads the WTA with 37 match triumphs this year but could not claim the crown in her first event since cracking the rankings top five, losing to Azarenka for the fourth time.
"She has had such good results. I'm so happy at how I played against her," Azarenka said. "I started to move a litle better as the match went on and I improved my defensive game and that helped my offensive game move forward."
Azarenka, ranked 18th, has stressed her return skills and pounced upon French Open runner-up Stosur's second serves to take command.
"I'm pretty good on the return," she said. "That's the big key. I have been practicing reaction on the return. If you react well you can return well."
Azarenka, who ousted 2009 Stanford winner Marion Bartoli of France in the quarter-finals, improved to 18-5 this season on hardcourts, the surface where she has won her three career WTA titles.
Azarenka broke Stosur three times in the first set for a 5-2 edge and held at love to claim the set, then kept the Aussie at bay in the second set as well.