Zvonareva had to recover from a 4-2 deficit in the first set but soon stepped up the pace and ran out a convincing winner over her unseeded opponent.
The 26-year-old Muscovite, a tearful loser in the finals of Wimbledon and the U.S. Open last year, sealed the win on her second match point with a thumping forehand crosscourt winner.
"I learned a lot over the last two grand slams," said Zvonareva. "I think I know myself a little bit better now. Hopefully that experience will help me to play my best tennis when I need it."
In Image: Leander Paes of India, left, and compatriot Mahesh Bhupathi talk as they play Spain's Tommy Robredo and Marcel Granollers during their third round match at the Australian Open tennis championships in Melbourne, Australia, Monday, Jan. 24, 2011.
Full Coverage: Australian Open 2011