Williams, currently ranked No. 29, needed just over an hour to defeat the Australian on a chilly day.
"I feel really good," said Williams, playing in her fourth tournament after being sidelined earlier this year with a wrist injury. "I don't think of myself as an underdog. I just think of myself not being as highly ranked as I should be and that happens when you take time off."
No. 10 seed Tatiana Golovin, who won for the first time last week at Amelia Island, advanced with a 6-4, 6-1 victory over Dominika Cibulkova.
"I've never really played back-to-back tournaments after winning one," Golovin said. "We left right after the tournament and we got here, and yesterday I had to rest to get ready to play today."
Golovin said she felt confident, but struggled because she was tired.
"You know what you can do and I'm playing well," said Golovin, who was treated for a blister during the match.
"It's just a matter of how I'm going to be able to hold up physically."
Top-seeded Nicole Vaidisova, ranked No. 8, was to meet Michaella Krajicek later Tuesday.
Serena Williams, ranked No. 11, was to meet qualifier Chan Yung-Jan in an evening match.
The Williams sisters could face off in the third round if they continue to advance.
In other matches, Francesca Schiavone advanced 6-2, 2-0 when Virginia Ruano Pascual retired with a back injury.
Virginie Razzano defeated Meghann Shaughnessy 6-3, 6-4; Katrinia Srebotnik defeated Julia Vakuleno 1-6, 6-2, 6-4 and Gisela Dulko beat Julia Schruff 1-6, 6-4, 6-4.