Kerber faced three set points trailing 5-2 in the second, and two more at 5-4, but turned the set in her favour by cutting loose and swinging for the fences, storming home to clinch the match and setting up a semi-final against Briton Johanna Konta.
"I played very well. I mean, I was playing my game from the first point," the smiling German told reporters. "When I was down 2-5, I was actually playing more aggressive.
"I think I won the match. She didn't lose it; I actually won it."
Kerber, seeded seventh and a semi-finalist at the 2011 U.S. Open and Wimbledon in 2012, was not the favourite against the 14th seeded Azarenka, who had won their six previous meetings including the Brisbane International final in the leadup to Melbourne Park.
While Kerber has struggled at times in the tournament, saving a match point in her first round clash against Misaki Doi, Azarenka bulldozed her way through the draw and looked to be back at the level that netted her Melbourne Park titles in 2012 and 2013.
But the Belarusian, who had lost just 11 games in her previous four matches, found herself 4-0 down in the first set, which Kerber went on to take in 48 minutes.
Azarenka reduced the error count and mounted a comeback that gave her the chance to serve out the second set at 5-2, but Kerber hit back, saving three set points and then two more in the 10th game to level it at 5-5.
Kerber kept up the pressure, drilling the lines and smacking winners from every angle before clinching the match in one hour, 45 minutes.
The German said she had visited Steffi Graf in Las Vegas last year to seek some advice from the 22-times grand slam champion and was inspired by her compatriot.
"Steffi is a champion. She won everything. She's a great person as well. I was able to practice with her a few days just before Indian Wells last year," Kerber said.
"But she taught me actually that I'm on a good way and try to believe in myself."
(Editing by Peter Rutherford)
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