The 6-3, 3-6, 7-6 (6), 7-6 (4) win allowed Nadal to join Jimmy Connors in third place on the all-time list of Grand Slam quarterfinal appearances, behind only Roger Federer (57) and Novak Djokovic (46).
Nadal was broken while serving for the match, then was unable to convert two breakpoints in the next game but held his composure to clinch it in a tiebreaker. The 19-time major champion won the Australian Open in 2009 and has reached four finals here times since. He will next play fifth-seeded Dominic Thiem, who is into the quarterfinals in Australia for the first time.
Alexander Zverev ended Andrey Rublev's 15-match winning streak and moved into the quarterfinals with a 6-4, 6-4, 6-4 win over the Russian player at Melbourne Arena.
Rublev hadn't lost a match since October, having won four matches at the Davis Cup finals and winning titles in Doha and Adelaide to start this season.
It is the first Australian Open quarterfinal for Zverev, and his third at a Grand Slam event. The seventh-seeded Zverev will next play 2014 Australian champion Stan Wawrinka.
There will be a first-time Australian Open champion in the women's draw.
Anastasia Pavlyuchenkova recovered from giving up a big first-set lead to beat Angelique Kerber 6-7 (5), 7-6 (4), 6-2 to reach the quarterfinals at Melbourne Park for the second straight year.
Pavlyuchenkova led 5-2 in the first set before 2016 Australian Open champion Kerber began a comeback that saw her win the opening set in a tiebreaker. But Pavlychenkova took the second in a tiebreaker and then broke serve immediately on the way to a 4—0 lead in the third.
Pavlyuchenkova, who took out No. 2 Karolina Pliskova in the third round, will next play Garbiñe Muguruza, who beat 9th-seeded Kiki Bertens 6-3, 6-3.
Kerber was the last former Australian titlist left in the draw.
Stan Wawrinka has advanced to the Australian Open quarterfinals with a five-set victory over fourth-seeded Daniil Medvedev.
The 2014 Australian Open champion dominated the fourth-set tiebreaker and then broke Medvedev in the opening game of the deciding set. He won 6-2, 2-6, 4-6, 7-6 (2), 6-2.
Medvedev's only other loss so far in 2020 was to Novak Djokovic in the ATP Cup. Wawrinka will play either Alexander Zverev or Andrey Rublev in the quarterfinals.
Medvedev was given an unsportsmanlike conduct warning in the final set when he became upset with the umpire when he wasn't allowed to challenge a call.
It was his 300th tour-level win on hard courts.
Bob and Mike Bryan have lost their third-round doubles match in their last trip to the Australian Open.
The U.S. twins, six-time champions in Australia, lost 6-3, 6-4 to fourth-seeded Ivan Dodig and Filip Polasek.
The 41-year-old Bryans, who first played at Melbourne Park in 2000, are planning to retire at the end of this year. This was their 85th Grand Slam tournament as a team. They have combined for 16 Grand Slam doubles titles and reached 30 finals at the majors, and are the most successful doubles combination of all time.
Two-time Grand Slam champion Garbiñe Muguruza has moved into the quarterfinals of the Australian Open with a 6-3, 6-3 win over ninth-seeded Kiki Bertens.
Muguruza won the 2016 French Open and 2017 Wimbledon. She is unseeded at a Grand Slam tournament for the first time since the 2014 French Open, when she was ranked 35th and also made the quarterfinals.
She came into the Australian Open after withdrawing from her quarterfinal match at the Hobart International due to a virus. But Muguruza says she is feeling better each day.
Muguruza will next play the winner of a later fourth-round match between Angelique Kerber and Anastasia Pavlyuchenkova.
Anett Kontaveit rallied from a set and a break down to beat 18-year-old Iga Swiatek 6-7 (4), 7-5, 7-5 and reach the quarterfinals of a major for the first time.
Kontaveit twice served for the match in the third set but finally clinched it when she broke Swiatek's serve.
The 28th-seeded Kontaveit will next play Wimbledon champion Simona Halep, who advanced over Elise Mertens in straight sets.
Two-time French Open runner-up Dominic Thiem has beaten Gael Monfils 6-2, 6-4, 6-4 to book a quarterfinal spot at the Australian Open for the first time.
It was Thiem's sixth consecutive victory over the French player, and made him the first player from Austria to make it to the quarterfinals at Melbourne Park since Stefan Koubek in 2002.
Thiem will play either top-ranked Rafael Nadal or Nick Kyrgios in the quarterfinals on Wednesday. Thiem has lost the last two French Open finals to Nadal and is 4-13 in their career meetings.
Wimbledon champion Simona Halep has reached the quarterfinals at the Australian Open with a straight-sets win over Elise Mertens.
Halep appeared to be cruising after winning the first set and going up a service break in the second, but Mertens broke back to level the second set at 4-4. Halep responded by converting her fifth break-point chance in the next game and served out at love to clinch the match. Halep will next play either Anett Kontaveit or Iga Swiatek.
No. 4-seeded Halep reached the Australian Open final in 2018 and won her first major title at the French Open that year.
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