The five-time Aussie Open and reigning U.S. Open chap Williams trailed late in the first set before ultimately taking a 7-5, 6-0 win over the unseeded Zvonareva of Russia. It marked a rematch of the 2010 Wimbledon final between the two, a match also captured by the American.
Williams said Zvonareva, a two-time Grand Slam finalist who played only five tournaments in 2014, started out aggressive "and I was a little too passive."
So she told herself: "'You know Serena, you've done so well here, you have nothing to lose.'"
Zvonareva won only eight points in the lopsided second set.
Up next for Williams will be Ukrainian Elina Svitolina.
The fourth-seeded Kvitova, fresh off her title in Sydney last week, took care of German Mona Barthel 6-2, 6-4, while sixth-seeded former Wimbledon finalist Agnieszka Radwanska dispatched Swede Johanna Larsson 6-0, 6-1 on another hot day at Melbourne Park.
Up next for the two-time Wimbledon champ Kvitova will be rising American Madison Keys, while Radwanska will take on American Varvara Lepchenko. Keys pulled off a minor upset of 29th-seeded Aussie Casey Dellacqua, 2-6, 6-1, 6-1.
In the marquee match of the day, the unseeded two-time Aussie Open champ Azarenka vanquished the eighth-seeded U.S. Open runner-up Wozniacki 6-4, 6-2.
Wozniacki said she's feels "cursed" at the Aussie Open. She also said while losing "sucks" she felt her good friend Azarenka was back to her best already after missing plenty of action last year due to injuries.
"Her level, it's high," Wozniacki said. "I think she's at the level that she left when she stopped playing."
Azarenka and Wozniacki have now split eight career meetings. Wozniacki got the better of Azarenka in the third round at the 2008 U.S. Open in their lone previous Grand Slam matchup.
Azarenka titled in Melbourne back-to-back in 2012 and 2013 before being slowed by a foot injury last year.
"I knew that I'm unseeded so I can play anybody. I just accept whoever is on the opposite side (and) I'm happy with the way I stayed consistent throughout the whole match," she said.
"I think there's always things you can improve, but it's a great progress from one match to another."
Azarenka's third-round opponent will be Czech Barbora Zahlavova Strycova.
Serena's 18th-seeded sister, Venus, who was the 2003 Aussie runner-up to her sibling, defeated fellow American Lauren Davis 6-2, 6-3. Venus has yet to lose this year, going 7-0, including a title in Auckland, where she upset Wozniacki in the final.
Venus will face Italian Camila Giorgi this weekend.
Eleventh-seeded Slovak and last year's Aussie runner-up Dominika Cibulkova moved on by downing Bulgarian Tsvetana Pironkova 6-2, 6-0, while American Coco Vandeweghe upended 20th-seeded former U.S. Open champion Samantha Stosur 6-4, 6-4. Stosur has never reached a quarterfinal at her home major, where she's competed every year since 2005, with the exception of 2008.
Cibulkova was last year's Aussie runner-up to the since-retired Li Na.
Meanwhile, 19th-seeded Alize Cornet defeated Denisa Allertova 6-4, 6-7 (2-7), 6-2; 24th-seeded Garbine Muguruza dropped Daniela Hantuchova 6-1, 1-6, 6-0; a 25th-seeded Zahlavova Strycova moved past Kai-Chen Chang 6-1, 7-5; the No. 26 seed Svitolina worked past Nicole Gibbs 7-6 (7-3), 7-6 (8-6); and a 30th-seeded Lepchenko defeated Ajla Tomljanovic 6-1, 7-6 (7-1). Lepchenko will face Radwanska on Saturday.
Additional second-round results saw Giorgi ease past Tereza Smitkova 6-1, 6-4, Swiss Timea Bacsinszky beat Anna Tatishvili 6-7 (5-7), 6-3, 6-2, and American Madison Brengle cruise past compatriot Irina Falconi 6-1, 6-3. Brengle reached her first-ever WTA final in Hobart last week and will meet another fellow American, Vandeweghe, in the round of 32.
In some third-round action on Friday, second-seeded Maria Sharapova will face 31st-seeded Kazakhstani Zarina Diyas; third-seeded French Open runner-up Simona Halep will meet American Bethanie Mattek-Sands; seventh-seeded Wimbledon runner-up Eugenie Bouchard will be opposed by France's Caroline Garcia; and 10th-seeded Russian Ekaterina Makarova will battle 22nd-seeded rising Czech Karolina Pliskova, last week's Sydney runner-up to Kvitova.
The former No. 1 and reigning French Open champion Sharapova was the Aussie champ in 2008 and runner-up in 2007 and 2012.