The win saw Serena extract some revenge on behalf of her sister Venus. Photograph: Jason O'Brien/Action Images

Serena Williams produced her best performance of the Australian Open so far to beat Spain's Carla Suárez Navarro 6-0, 6-3 and keep her title defence on track. The top seed and four-time champion, who played well within herself in her first two matches, upped her intensity to advance to the fourth round in 81 minutes.

For all of Suárez Navarro's craft and guile, the 32nd seed, who knocked Serena's sister Venus out in the second round last year at Melbourne Park, was unable to match the defending champion's power.

Serena's only real difficulty was in closing out the first set, needing eight set points in a game that went to deuce 13 times and lasted longer than the previous five games combined. "It was definitely the toughest 6-0 set," she said. "I thought, 'OK, Serena, don't put too much pressure on this. Worst case scenario it will be 5-1.' But way to keep fighting."

The world No1 will now meet the Australian 13th seed, Sam Stosur, who opened play on the Rod Laver Arena with a 6-4, 6-1 win over Italy's Alberta Brianti. "I'm looking forward to it," said Stosur. "I've lived up to my expectation and I've got to where I should have got to.

"Playing the No1 player in the world, defending champion, I can go out there and really enjoy it. I know I won the last time we played against each other [at Stanford in 2009]. That's probably not going to mean too much going into Monday's match, but at least I know I've been able to beat her before."

Victory for Serena against Stosur could potentially leave her one more win away from an all-Williams semi-final. Venus had a tougher time today but still managed to see off Australia's Casey Dellacqua 6-1, 7-6, closing with an ace on her fourth match point.

Venus will now play Italy's Francesca Schiavone as she looks towards a clash with Serena - and beyond. "Of course I want to progress well to the final, that is my goal," said Venus, who lost the 2003 Australian Open final to her sister. "So far, I'm getting closer. You know how it works. Just got to play well every match."

Other winners on day six included the seventh seed, Victoria Azarenka, and last year's US Open finalist, Caroline Wozniacki. Under the Hisense Arena roof, which was closed following an early rain shower, Azarenka outclassed Tathiana Garbin 6-0, 6-2 to set up a last-16 match with Russia's Vera Zvonareva. Under the Rod Laver lights, Wozniacki rounded off the day's play as she eased past Israel's Shahar Peer 6-4, 6-0. The world No4 will next face China's Li Na.