So it was early, with Zvonareva threatening to break Williams' serve at 15-40 after taking a 5-3 lead in the first set. The world No1 smacked two powerful forehand winners to reach deuce, but was again facing set point.
Williams held, broke back twice and then dished out a bagel as she wrapped up the second set in just 27 minutes.
The 18-time grand slam champion next faces unseeded compatriot Nicole Gibbs or the 26th seed, Ukraine's Elina Svitolina.
Dominika Cibulkova, last year's finalist who is seeded 11th, crushed Tsvetana Pironkova 6-2, 6-0 to join Williams in the third round.
Earlier yesterday, Venus Williams and Agnieszka Radwanska both sailed into the third round in straight sets. Sixth seed Radwanska needed only 44 minutes to dismiss Johanna Larsson 6-0, 6-1 on Rod Laver Arena, setting up a clash with Varvara Lepchenko.
Williams was not quite as ruthless in her all-American outing against Lauren Davis, but still a comfortable 6-2, 6-3 winner on Margaret Court Arena.
Williams, the 2015 Auckland ASB Classic champion who is seeded 18th, recovered well after dropping her opening service game in both sets.
Williams broke her compatriot's serve five times, charging to victory in an hour and 16 minutes as Davis bounced her racket in anger.
The pair had met only once before - in Auckland earlier this month, when Williams won their semifinal in straight sets.
The 34-year-old seven-times grand slam champion went on to defeat Caroline Wozniacki in New Zealand, suggesting she could do some damage at Melbourne Park.
Williams next faces Italy's Camila Giorgi.
"She definitely raises her game depending on the calibre player that she plays," Williams said.
"It's just important to remain consistent and aggressive, just as I've been this whole year."
Meanwhile, Spanish 24th seed Garbine Muguruza downed Daniela Hantuchova 6-1, 1-6, 6-0. the second set was but a blip.
Men's No1 Novak Djokovic had an easier run, spending a minute less than Williams on Rod Laver Arena in his 84-minute, 6-0, 6-1, 6-4 win over No 88-ranked Andrey Kuznetsov. Defending champion Stan Wawrinka advanced to the third round for the seventh consecutive year with a 7-6 (4), 7-6 (4), 6-3 win over No. 194-ranked qualifier Marius Copil.
- AAP/AP