Azarenka was awarded $1 million, the richest winner's checks in the tournament's history. Sharapova earned $500,000.
Azarenka broke Sharapova six times in improving her record to 23-0 this year, the best start to a season since Martina Hingis went 37-0 to open 1997. The top-ranked Belarusian won her Tour-leading fourth title of the year.
"It's important to stay humble and to know that what I have been doing is working," Azarenka said. "Don't forget those little details, and being disciplined, professional off the court is as important as being determined and really hard working on the court."
The women's final was a rematch of the Australian Open final, which Azarenka won 6-3, 6-0 in January to keep Sharapova from regaining the No. 1 ranking. This time, Sharapova was error-prone during the 1½-hour match on an unusually cold, windy day in the desert. The second-ranked Russian kept hitting close to the lines and missing.
"She's extremely solid and she makes you work for every point," Sharapova said. "Maybe she forces you to want to do a little bit more than either you should or would want to. She's really fit, playing with a lot of confidence, and you can definitely sense that when she's moving around the court and hitting the ball. I just made too many unforced errors at the wrong time and wasn't solid enough."
Azarenka broke Sharapova in the final game, when the Russian double-faulted then shanked a forehand to set up Azarenka's first match point. She won after forcing Sharapova into a desperation defensive shot that sailed beyond the baseline. Azarenka dropped her racket, pumped her right arm and broke into a brief dance while smiling broadly.
She joked that the best thing about being No. 1 is "you don't really have to find yourself in the draw anymore. It's the first one."
It was yet another dominant performance by Azarenka, who improved to 5-3 against Sharapova, including 4-0 in finals. Sharapova hasn't beaten Azarenka in a completed match since 2009; she won last year in Rome when Azarenka retired in the second set with a right elbow injury.
"What was important for me was to try to put as much pressure on her, not to really let her into the match because when she has a little window open she always going to take the opportunity and she's going to fight no matter what the score is," Azarenka said.
"I really had to stay on my feet and keep putting that pressure and playing my game. It was a little bit difficult with the wind to control, but I handled the situation really good, and I'm really happy that I went through with this determination."
Sharapova twice had aces to hold serve in the first set, but her groundstrokes were inconsistent. Azarenka led 4-1 in the second set when Sharapova won two straight games to get to 4-3, capped by a swinging forehand volley winner. But Sharapova won just two points in the final two games to fall to 13-3 on the year.
"I still don't think I was as aggressive as I should be," Sharapova said. "But it's okay. We're going to play against each other a few more times, so I'll have time to change that."
Information from The Associated Press was used in this report.