Stosur, whose last win was the 2011 US Open, also beat world number four Agnieszka Radwanska in the quarter-finals and said the tournament had given her a massive of confidence.
"I think winning tournaments is the absolute proof that you're a good player and you're able to beat whoever you come across," Stosur told reporters.
"I know I've only won four in my career. But I know how I'm capable of playing and doing what I can do, then I know I've got a chance. I guess this week kind of helped prove that.
"It's great to be able to have now two top five wins in a week when I hadn't had one in quite a while. That is a huge confidence boost."
Stosur came into the final with an 0-8 record against Azarenka, but largely took the racquet out of the Belarusian's hands with huge serves and big forehands.
She said she had never doubted her ability to finally get past the former world number one.
"I guess it's a different psyche each time you play someone," she said. "I went through something similar when I played Maria Sharapova a bunch of times. I think it took 10 times for me to be able to beat her.
"I knew it was possible one day against Vika, but the last two matches that we played have been very, very close. I felt like I was almost in winning positions with those two.
"So I think going into today there was no reason to believe that I wasn't going to be able to turn that result around and win today. It's a matter of playing well and doing it when it counts."
After losing to Russian Olga Govortsova in her opening round at the Stanford Classic, Stosur was not sure whether she should request a wild card into the Carlsbad Open.
She faced the same scenario in 2011, when she decided not to take a wild card into Carlsbad and went on to beat Serena Williams to win the US Open final.
"I knew that that was the past," Stosur said. "My coach David Taylor and I spoke about all the pros and cons. You can practice all you want, but at some point you got to put it into play in matches.
"That's why I came, and obviously now very, very pleased with that decision."
(Editing by Peter Rutherford)
