Melbourne, Australia — Venus Williams continued her resurgence at the Australian Open with a 6-3, 2-6, 6-1 win over sixth-seeded Agnieszka Radwanska on Monday to reach the quarterfinals of a Grand Slam for the first time since 2010.

The 34-year-old, seven-time major winner joined her younger sister, Serena, in the quarterfinals. The sisters haven't both reached the last eight at a major since Wimbledon that year.

Her inspiration? "Definitely my sister Serena, she's just the ultimate champion," Venus Williams said. "And definitely a lot of inspiration from all my fans who have stayed behind me through thick and thin."

Venus Williams, who has been dealing with an energy-sapping illness for the last four years, will next face Madison Keys, a 19-year-old American who was inspired to play tennis by watching the Williams sisters.

Top-ranked and 18-major winner Serena, motivated by a Grand Slam loss that stung her more than most, dug deep for a 2-6, 6-3, 6-2 comeback win over Garbine Muguruza in the afternoon before returning to watch her sister in the night match on Rod Laver Arena.

She had been pushed for 2 1/2 sets by No. 24-seeded Muguruza, who matched her in the heavy-hitting stakes, and who had conceded only four games to her in a second-round upset last year at the French Open.

"She made me play a lot better. I had to play the best match of the tournament or else I was going to be out," Williams said. "She was just hitting winners like left and right. Every shot I hit, she basically hit a winner on. So I had to change my approach."

The five-time Australian Open winner next faces Dominika Cibulkova, who reproduced the kind of tennis that took her to the final here last year as she beat two-time champion Victoria Azarenka 6-2, 3-6, 6-3. Keys advanced to her first Grand Slam quarterfinal with a 6-2, 6-4 win over good friend and fellow American Madison Brengle.

"It's a huge opportunity for me. I'm going to make the most of it," she said. "I want Io be at the end of the tournament holding the trophy up. That's my goal in the long run."

Defending champion Stan Wawrinka beat Guillermo Garcia-Lopez 7-6 (2), 6-4, 4-6, 7-6 (8) to move into the men's quarterfinals, where he'll play U.S. Open finalist Kei Nishikori. No. 8 Milos Raonic advanced with a 6-4, 4-6, 6-3, 6-7 (7), 6-3 win over No. 12 Feliciano Lopez to reach the last eight in Australia for the first time.

Spurred on by hundreds of flag-waving Japanese supporters at Rod Laver Arena, No. 5-ranked Nishikori had little trouble in a 6-3, 6-3, 6-3 win over No. 9 David Ferrer, who reached the French Open final and Australian Open semis in 2013.

Nishikori's routine win was unlike the three-setter Williams endured, when she appeared to be laboring and had a serious cough. Williams struggled with her serve in the first set, winning only one of a dozen points on her second serve. She couldn't convert her six break-point chances, while Muguruza broke her twice.

"She hits the ball really, really big, really, really hard," Williams said. "Someone in the crowd was like 'C'mon Serena use spin' and I was like 'OK.' There's coaches everywhere out here! Thank you."

Serena Williams hasn't advanced past the quarterfinals at Melbourne Park since winning her last title here in 2010. She went out in the fourth round last year, and followed that up with the 6-2, 6-2 loss to Muguruza at Roland Garros — her most lopsided loss at a major.

She had difficulty breathing at times Monday, and coughed throughout.

"When I got down, I was thinking, 'What can I do now?'" Williams said. "Whatever happens, I thought, I've won this five times."

She gradually picked up power in the second set, broke for a 5-3 lead and then fired three aces and a service winner to level it.

After missing break points on Muguruza's serve in the opening game of the third, Williams saved six break points and needed almost 13 minutes to hold.

Her confidence up, Williams broke for a 3-2 lead and dominated the rest of the match.

She'll need every bit of confidence against the 1.61-meter (5-foot-3) Cibulkova, who pounded 44 winners and broke former No. 1-ranked Azarenka's serve seven times. The No. 10-ranked Cibulkova lost the final here last year to the now-retired Li Na, and is back in that kind of form.