Sharapova topped Azarenka 6-4, 6-2 and will face Serena Williams, who breezed past Agnieszka Radwanska 6-2, 6-1 in 61 minutes.
Sharapova dominated the match, breaking serve twice while winning the first four games of the second set.
"I certainly didn't make as many mistakes today as I did in our previous matches," said Sharapova, who was 1-4 against Azarenka this year coming into Saturday's match. "I also returned a little bit better, although I still feel like I could have returned better than I did today."
Williams had little trouble against the weary Radwanska, winning 10 of the final 11 games in the contest.