Azarenka had never taken a set off Zvonareva in their four previous meetings and looked to be heading for another quick defeat when she lost the opening set and went a break behind in the second.
But the 20-year-old, ranked seventh in the world, turned the match around by winning all the remaining games to seal victory after nearly 2-1/2 hours at the Rod Laver Arena.
“She played good, I just tried to keep fighting even when I was down,” Azarenka said in a courtside interview. “I knew I could stay with her. I just had to believe in myself.”
Azarenka won the Australian and U.S. Open junior titles in 2005 and made the final eight at the French Open and Wimbledon last year.
But she faces a daunting task reaching her first grand slam semi-final with her next match against defending champion Serena Williams, who defeated Australia’s Samantha Stosur 6-4 6-2.