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Naomi Osaka saved two match points and Serena Williams was taken to three sets as two of the favourites reached the Australian Open quarter-finals.

Having lost the opening set to Garbine Muguruza, Japan's Osaka was a break down in the second and faced two match points at 5-3 in the third.

But she won four games in a row to win 4-6 6-4 7-5 against the Spaniard, who is also a former world number one.

Williams then came through 6-4 2-6 6-4 against Belarusian Aryna Sabalenka.

The American surged into a 4-1 lead in an entertaining final set, before 22-year-old seventh seed Sabalenka broke back and levelled at 4-4.

But Williams held serve and then broke her opponent's serve to clinch the win and keep alive her hopes of a record-equalling 24th Grand Slam singles title.

"I am happy to get through that one because it wasn't easy," the 39-year-old 10th seed said. "I felt like I was there, even the games I lost were super close and just one shot here or there."

Williams will face second seed Simona Halep, who recovered to beat 19-year-old French Open champion Iga Swiatek 3-6 6-1 6-4.

It was the second successive match in which the Romanian has had to come from a set down, but she found form in the second set to edge past the Polish teenager in one hour and 50 minutes.

Halep said it was "tough" to think about playing Williams, whom she beat in the 2019 Wimbledon final.

"I will try to enjoy myself and I can only beat Serena if I play my best," she said.

Osaka, who won the second of her three Grand Slams at the Australian Open in 2019, will face Hsieh Su-Wei in the last eight.

The Taiwanese 35-year-old beat 19th seed Marketa Vondrousova 6-4 6-2 to become the oldest player to make a Grand Slam quarter-final debut in the Open era.

"I just knew it was going to be tough," said 23-year-old Osaka, who was facing 14th seed Muguruza for the first time.

"I feel like I was a bit intimidated because I knew that she was playing really well coming into this match. I feel like in the stressful points I just had to go within myself."