Her win at Ken Rosewall Arena came moments after Safina finished off a 6-3, 6-0 win over fellow Russian Vera Dushevina in just over an hour on Court 1 at the Olympic Park Tennis Centre.
Williams said she was much more comfortable with her game Tuesday.
"I still think I can improve on some things, and that's what I want to do," Williams said. "I don't want to peak too soon. I just want to stay level for the whole season."
Four other seeded players in the women's draw at the joint ATP-WTA tournament also advanced Tuesday.
No. 3 Elena Dementieva of Russia beat Jarmila Gajdosova of Slovakia 6-2, 6-4 and No. 5 Svetlana Kuznetsova of Russia beat Estonia's Kaia Kanepi 6-2, 2-6, 7-6 (3). Sixth-seeded Agnieszka Radwanska of Poland defeated Slovakia's Daniela Hantuchova 6-3, 7-5 and Caroline Wozniacki of Denmark, the eighth-seeded player, beat Britain's Melanie South 6-2, 6-0.
Williams will play Wozniacki in the quarterfinals.
"Last I checked she was No. 12," said Williams. "She's probably even better now. It'll be a good match for me going into the Australian Open, and also for her as well."
Former No. 1 Lleyton Hewitt of Australia continued his comeback from a five-month injury layoff to beat Frenchman Julien Benneteau 5-7, 6-2, 6-4 and Paul-Henri Mathieu of France beat Italy's Andreas Seppi 6-2, 2-6, 6-3.
Hewitt, who plays Tipsarevic in the next round, has won the Sydney title four times and had a 20-match winning streak at the 2000 Olympic venue. The win maintained Hewitt's record of never having lost a first-round match in 19 tournaments in Australia.
"It was always going to be tough in the first sort of tournament match back for a while," said Hewitt, who had hip surgery in August.
"It's not easy to come out in match situations and just pick it up straightaway, doesn't matter how good you are. It's a matter of getting that confidence."
In later matches, two French players advanced. Richard Gasquet beat defending champion Dmitry Tursunov of Russia 7-6 (4), 6-4 and Jeremy Chardy won his match over Radek Stepanek of the Czech Republic when Stepanek, who won last week's Brisbane International final, retired due to a flu-like illness when trailing 6-4, 3-0.
"I'm disappointed I could not finish today," Stepanek said. "I felt OK this morning but after about four games into the match I started to feel unwell, and that affected the way I was playing. After such a great week in Brisbane, I was really hoping to be able to do it again in Sydney."
The top four men's seeds -- Novak Djokovic, Gilles Simon, Jo-Wilfried Tsonga and David Nalbandian -- received first-round byes. Djokovic, who begins the defense of his Australian Open title next week in Melbourne, plays Mathieu on Wednesday.