World No.1 Serena Williams has come back from a set down for the second straight match at the Australian Open, beating Spaniard Garbine Muguruza to advance to the quarter-finals.

Williams started slowly but finished strongly against the 24th-seeded Muguruza to win 2-6 6-3 6-2 in a seesawing fourth-round match lasting two hours on Monday.

Her reward is a last-eight showdown against 2014 Open runner-up Dominika Cibulkova, who also needed three sets before seeing off the challenge from Victoria Azarenka 6-2 3-6 6-3.

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Williams is chasing a sixth Australian Open title and a first since 2010.

She and Muguruza had split their previous two encounters – both of which were one-sided, in sharp contrast to Monday’s marathon encounter.

“She did everything she needed to in the first set,” said Williams of Muguruza.

“I decided to do my best, stay focused and relax.

“She hits the ball really, really big and really hard.”

Dominika Cibulkova’s love affair with the Australian Open continues.

Williams had also dropped the first of her third-round clash against Ukraine’s Elina Svitolina.

For the second straight year, the diminutive Cibulkova is making a run deep into the Australian Open, with the No.11 seed from Slovakia charging into the last eight with victory over two-time Open champion Azarenka.

After battling injuries and personal issues in 2014, the Belarusian entered the first grand slam of the year without a seeding, although she shaped as the most dangerous floater in the draw.

But it was Cibulkova who triumphed on Monday, winning in two hours and 10 minutes.

Cibulkova’s best-ever performance at a grand slam came last year at Melbourne Park when she advanced all the way to the final before losing to China’s Li Na.

“I just walk on the court here and all the great memories came through my mind,” said the 25-year-old Cibulkova on Monday.

“I just have to believe in myself and that’s what I’m doing right now.”

Free-swinging Madison Keys advanced to her first major quarter-final with a comprehensive 6-2 6-4 victory over namesake and fellow American Madison Brengle.

Keys completed dominated the winners’ count 38-3, progressing to a last-eight clash against either fellow American Venus Williams or Polish No.6 seed Agnieszka Radwanska.

-AAP