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The 19-year-old scored her first top-tier title in one hour and11 minutes to stop Williams from winning her record sixth title at Key Biscayne as she never looked comfortably with strap on her left thigh.
Williams admitted that she even considered pulling out of the final.
"I thought about it. I don't like to not play but I definitely thought about it," said Williams.
With the win, Azarenka will move up to eighth in the new world rankings as she has secured her third title of the year following victories in Brisbane and Tennessee.
"I've improved almost everything since last year but most of all I am believing in myself a little more, believing I can win tournaments," said Azarenka.
The 11th seed teenager broke serve to go 2-1 up in the first set but was broken straight back. Later on, she pushed Williams wide and looked strong on her forehand as she broke twice at the end of the set.
The second set became a sure bet for the teenager as Williams appeared to be knocked out of the fight.
Last time the pair met, in the fourth round of the Australian Open, Azarenka won the first set but then retired due to illness.