The 22-year-old Belarusian dropped her opening service game and was down 2-0 after a nervous start before winning 12 of the next 13 games to take the match away from Sharapova, a three-time major winner and the 2008 Australian champion.
She became only the third woman to earn the No. 1 spot after winning her first Grand Slam title. And she's the fifth different winner in as many majors.
Caroline Wozniacki vacated the top spot when she lost in the quarterfinals, leaving both Azarenka and Sharapova to battle it out for the title and the top ranking.
The third-seeded Azarenka set up championship point with a stunning forehand winner and sealed it when Sharapova netted a backhand.
She dropped on to her knees at the baseline with her hands over her face. She got up, held up her hands and mouthed "What happened?" before jogging up to her coach, Sam Sumyk, in the stands to celebrate.
"The best feeling, for sure," Azarenka said. "I don't know about the game. I don't know what I was doing out there.
"It's just pure joy what happened. I can't believe it's over."
At the trophy presentation, her first word was "wow." Then she started giggling. She thanked her support team, saying "You made me realize I can believe in myself and I can finally raise this trophy."
And she paid special credit to her grandmother, "the person who inspires me the most in my life."
Azarenka has been a distinctive presence at Melbourne Park as much as for her shrieks and hoots with each shot and seemingly boundless energy as for her white shorts, blue singlet and lime green head and wrist bands.
Against Sharapova, she maintained the frenetic movement that has been the hallmark of her campaign in Australia, her 25th consecutive major. She won the Sydney International title the weekend before the season's first major and is now on a 12-match winning streak, including a semifinal win against 2011 Australian Open champion Kim Clijsters. She's the first player since 2004 to win a WTA tour event the week before winning a major.
A lot of attention before the final was on the grunting of both players. In the second game someone shouted "turn the volume down," but there was nothing after that except for a few mutterings when the shrieking got really loud.
Finishing off the match in 1 hour, 22 minutes at Rod Laver Arena seemed to silence the critics.
"She did everything better than I did today. I had a good first couple of games, and that was about it," Sharapova said. "Then she was the one that was taking the first ball and hitting it deep and aggressive. I was always the one running around like a rabbit, you know, trying to play catch-up all the time."
Sharapova also took only three games in a 2007 final loss to Serena Williams, who also conceded only three games in the 2009 final against Dinara Safina in two of the other previously lopsided finals at Melbourne Park.
When Sharapova won the first two games, there was no indication of how lopsided the match would be. She had the experience of five previous Grand Slam finals, including the most recent at Wimbledon last year. But it was Azarenka who took control after holding for the first time, breaking Sharapova at love and then holding again on a three-game roll.
Sharapova held, finishing off with an ace, to level at 3-3 in the first set but didn't win another game.
Azarenka started dictating the points, coming to the net at times, hitting winners from the baseline and forcing the 24-year-old Russian to the extremes on both sides of the court. Sharapova seemed barely able to move by comparison, and had 30 unforced errors in the match.
The second set was completely lopsided and lasted only 36 minutes, with Sharapova winning only 12 points in six games.
"As in any sport, you have your good days, you have your tough days and you have days where things just don't work out," said Sharapova, who has now been on the losing end of two of the most lopsided scorelines in a final at Melbourne Park.
When the new list is released Monday, Azarenka will be the 21st woman to hold top spot since the computer rankings were introduced in 1975. She's also the fourth different woman to win their maiden Grand Slam title in the last four majors, starting with Li Na's win at the French Open, and followed by Petra Kvitova's title at Wimbledon and Sam Stosur's win at the U.S. Open.
Azarenka had momentarily flirted with quitting the sport during a quick trip home to Minsk after a loss at Doha early last year. But she was quickly set straight by her family, including her grandmother, who had reportedly worked three jobs to the age of 71.
She couldn't get through to her family immediately "because my phone is freaking out right now," but she texted them from the court.
"I made a pretty smart decision, not walking out, right? That was pretty special," she said. "There's always ups and downs, now I'm up."