The player Sharapova beat in last year's final, Sara Errani, also eased into the second round.
Azarenka beat Italian seventh seed 6-0 7-5 Sara Errani in their last four clash.
Errani, seeded No. 8, fell to 0-26 against opponents ranked in the top five.
Sharapova had the last laugh, whacking a forehand winner past Errani on match point.
She returned to the semifinals Wednesday despite a patchy performance, beating Sara Errani 7-5, 7-5.
Sara Errani and Roberta Vinci are due to play doubles against Anastasia Pavlyuchenkova and Nadia Petrova.
Henin will next play fellow Belgian Yanina Wickmayer, who defeated Italy's Sara Errani 6-1 6-7 (4-7) 6-3.
Both players smiled and laughed, and Errani raised her hands in mock celebration as the crowd cheered.
Tuesday's other quarterfinal will be between German 10th seed Angelique Kerber and Italy's No. 21 Sara Errani.
Last year's French Open finalist Sara Errani defeated 64th-ranked Jamie Hampton 6-2 6-1 in the opening match.
Fifth-seeded Italian Sara Errani also lost in three sets to 2012 runner-up Daniela Hantuchova 4-6 6-1 7-5.
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Sara Errani and Roberta Vinci beat Liezel Huber and Varvara Lepchenko 6-2 6-2 in the decisive doubles rubber.
Italy's Errani refused to capitulate in the second set, but was never able to threaten the Russian's dominance.
Errani and Francesca Schiavone then combined to beat Hradecka and Kveta Peschke (CZE) 6-2 6-4 in the concluding doubles.
Errani had also taken the doubles title and had been confident of victory.
Meanwhile, World No.7 Errani defeated her doubles partner Robert Vinci 6-3 6-3 following an hour and 23 minute battle.
Victor Sharapova made a point of praising Errani's achievement in reaching the final.
In the last game of the match, Errani hit two perfect drop shots, including one to save a match point.
While she and Errani waged a series of long, entertaining baseline rallies, both were also prone to blowing easy shots.
In the women's final, Italian top seed Sara Errani breezed past second seed Carla Suarez Navarro of Spain 6-0 6-4.
In the women's draw, second seed Maria Sharapova beat No. 6 Sara Errani in a repeat of the 2012 French Open.
Sharapova faced Errani in a rematch of last year's French Open final, which Sharapova won to complete a career Grand Slam.
Petrovic, ranked 36, now advances to the quarter-finals along with Italy's Sara Errani who beat Czech qualifier Renata Voracova 6-2 6-2.
Errani, also 25, had never advanced past the second round at the French Open before this year, despite a strong clay-court background.
The victory, which took two hours and 29 minutes to complete, was the second in successive tournaments for the Russian over Errani.
It was Sharapova's third successive win over Errani, having also got the better of the Italian at the season-ending WTA Tour Championships.
Errani will go into the final as favorite having won each of her three previous meetings against Kvitova without dropping a set.
Cibulkova has also registered victories over 2011 Wimbledon champion Petra Kvitova and 2012 French Open finalist Sara Errani at the Sydney event.
Williams knocked out underdog Errani in just over one hour, 6-1, 6-2.
Azarenka will take on Serena Williams in the final after the American made fast work of her semi-final defeat of Italy's Sara Errani.
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