SYDNEY, Australia — Top-seeded Serena Williams and No. 2 Dinara Safina made short work of their second-round opponents Tuesday to move into the Sydney International quarterfinals.

Williams, who was stretched to three sets and saved four match points in her opening match against Samantha Stosur of Australia, beat Sara Errani of Italy 6-1, 6-2 in 50 minutes Tuesday.

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."

In another match, Japan's Ai Sugiyama beat Anabel Medina Garrigues of Spain 2-6, 6-1, 6-2.

In first-round men's play, Janko Tipsarevic, cheered on by dozens of boisterous, flag-waving Serbian fans, defeated eighth-seeded Mardy Fish of the United States 6-4, 3-6, 6-4.

Australian Chris Guccione used the hometown crowd to his advantage to beat No. 6 Tomas Berdych of the Czech Republic 6-3, 6-4.

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.