Top-seeded Azarenka from Belarus beat German qualifier Dinah Pfizenmaier 6-1, 6-1 while Australian sixth seed Stosur saw off Irina Falconi of the United States 6-1, 6-4.
Azarenka is seeking to become the first woman since Jennifer Capriati in 2001 to win the first two Grand Slam tournaments of the year. “It was a different game for sure today,” Azarenka said.
“I didn’t really know my opponent and it took a few games to understand what she does. But after a few games I found my rhythm and definitely played much better today.”
Stosur was the runner-up here in 2010 when she was upset in the final by Francesca Schiavone of Italy.
Photos: Shah Rukh Khan, Shweta Bachchan at Karan Johar's book launch
Photos: Sunny Deol with sons Karan and Rajvir at Mumbai airport
Photos: 10 beautiful moments that capture winter around the world
Photos: Karisma Kapoor, Preity Zinta, Shraddha Kapoor at Mumbai airport
Spotted: Anushka Sharma and Diljit Dosanjh at Mumbai studio