The world number one's serve was far more consistent than in her previous match and she did not face a break point in taking the first set.
She was gifted the only break in the seventh game when Azarenka blasted a forehand wide down the line.
The American then sealed the set with an ace and an early end to the match seemed likely when she broke the Belarusian in the first game of the second set, but instead it brought her opponent to life.
Azarenka broke Williams twice to take a 4-2 lead but lost her own serve to restore parity.
In the crucial 11th game, Williams hit a vicious backhand down the line to secure her third break of the set and then served out for victory.
Her second set efforts showed Azarenka is not far off from toppling Williams, who she split four matches with last year, and after the match said: "I hope to meet you in Melbourne."
Williams is also eyeing another meeting between the pair before they leave Australia.
"I hope we do play in Melbourne too because that would mean we'd be going the farthest," Williams said.
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