Azarenka earned her 17th straight victory and first title since replacing Caroline Wozniacki atop the rankings after winning the Australian Open. It was her third title overall in 2012.
Azarenka showed no ill effects after twisting her left ankle in the semifinal against Agnieszka Radwanska on Saturday.
She broke the fifth-ranked Stosur twice to lead 4-1 in the first set, making a brief trip to the net to clinch it with a backhand volley. Azarenka cruised to victory after winning the first three games of the second set.
"It's amazing. I can't believe I could play that kind of tennis today," Azarenka said. "I knew I wouldn't be 100 percent, so I had to change and adjust. I was just surprised today that everything was going in."
Fearful of further aggravating her ankle injury, Azarenka said she tried to keep the rallies short and took advantage of the windy conditions. The ankle was wrapped during the match and Azarenka said it should be fine after a few days of rest.
"I was trying to be really aggressive and not to let her command it, because that's what she likes to do," Azarenka said. "She has a huge serve, and the first shot, that's what she puts the opponent on the run, and you run like so far behind the baseline. So I tried to take that away from her."
Azarenka improved to 6-0 against Stosur after having previously beaten the Australian in November at the year-ending WTA Championships.
She kept Stosur's potent kick serve in check with her return game, with the Australian winning only 50 percent of first-serve points and 48 percent on the second. Azarenka also displayed a range of shots and ran down most balls, and Stosur finished with 25 unforced errors to only eight for the Belarusian.
"She's very good at neutralizing everything," Stosur said. "Especially tonight, I feel like I didn't get rewarded for hitting big serves. I didn't get rewarded for stepping in and trying to crack the return."
Stosur said Azarenka is benefiting from a growing belief in her game that comes with winning her first Grand Slam title and the longest winning streak since Maria Sharapova's 18-match run in 2008.
"I think the biggest difference is probably just her confidence that she's playing with at the moment," Stosur said. "When you're like that, you seem to do everything a little bit better. ... Obviously I haven't had success, and hopefully tonight I have been able to learn a couple of things and I can go into the next one maybe with something else to think about."
Azarenka will play at the Dubai Championships next week in Doha, the place where she lost in the first round last year -- a defeat she said briefly led her to consider quitting tennis.
After a brief trip home and counseling from her mother and grandmother, she returned energized and with a more mature attitude. That resulted in her having the best season of her career, winning 55 of 72 matches to finish the year at No. 3.