Williams trailed late in the first set before ultimately taking a 7-5, 6-0 win over the unseeded Zvonareva of Russia.
It was a rematch of the 2010 Wimbledon final between the two, a match that Williams won 6-3, 6-2.
Serena's sister, Venus, who was a finalist at the 2003 Aussie Open, had a much easier time defeating fellow American Lauren Davis 6-2, 6-3.
Tournament officials confirmed on Wednesday that the Williams sisters pulled out of their doubles draw, but they did not specify a reason.
In other action, 24th-seeded Garbine Muguruza defeated Daniela Hantuchova 6-1, 1-6, 6-0, while Swiss Timea Bacsinszky beat Anna Tatishvili 6-7 (5-7), 6-3, 6-2 and Italian Camila Giorgi eased past Tereza Smitkova 6-1, 6-4.