Rafael Nadal outclassed Fabio Fognini to close in on the all-time Grand Slam titles record on Monday as Ashleigh Barty ramped up hopes of becoming the Australian Open's first home winner in 43 years.

Nadal said his lower-back stiffness was continuing to improve after his 6-3, 6-4, 6-2 against the flamboyant Italian, which set up a quarter-final against Greece's Stefanos Tsitsipas.

Spain's Rafael Nadal beat Fabio Fognini to reach the last eight
Spain's Rafael Nadal beat Fabio Fognini to reach the last eight AFP / Paul CROCK

Fognini had registered a five-set win over Nadal at the 2015 US Open, but the Spaniard cantered to victory after recovering from 2-4 down in the second set.

Nadal is now into his 43rd Grand Slam quarter-final, staying on course for a title match with eight-time winner Novak Djokovic who battled through an abdominal injury to reach the last eight on Sunday.

"I'm happy to be in the quarter-finals today -- that means a lot to me, it's positive stuff," said Nadal, who is level with Roger Federer on 20 Grand Slam men's singles titles.

Russia's Andrey Rublev went through against Casper Ruud of Norway
Russia's Andrey Rublev went through against Casper Ruud of Norway AFP / David Gray

Next up for Nadal is world number six Tsitsipas, who went through on a walkover after Italy's Matteo Berrettini pulled out with an abdominal strain.

The Melbourne tournament remained fan-free for a third day on Monday during a five-day lockdown in Victoria state to curb a coronavirus outbreak.

As the action continued in front of empty stands, top-ranked Barty beat big-hitting American Shelby Rogers in impressive fashion to reach the last eight.

Australia's Ashleigh Barty is the world number one
Australia's Ashleigh Barty is the world number one AFP / Brandon MALONE

Barty won 6-3, 6-4 to go into the quarter-finals without dropping a set as she bids to become the first Australian champion since Chris O'Neil in 1978.

"I love playing at home and sharing this with my friends and family," said Barty, who hit 21 winners.

The former French Open champion next plays Karolina Muchova, who came through two tight sets to beat Belgium's Elise Mertens 7-6 (7/5), 7-5.

Jessica Pegula of the US reached her first Grand Slam quarter-final
Jessica Pegula of the US reached her first Grand Slam quarter-final AFP / Paul CROCK

Earlier, unseeded American Jessica Pegula reached her maiden Grand Slam quarter-final with victory over Elina Svitolina, her first over a top-10 player.

Pegula, whose billionaire father owns the Buffalo Bills NFL team, overcame fifth seed Svitolina 6-4, 3-6, 6-3 to set up a meeting with fellow American Jennifer Brady, a 6-1, 7-5 winner against Croatia's Donna Vekic.

"I can't get more confident -- it is my best result yet and I'm playing good tennis and today was a hard-fought win," said Pegula, 26.

"Jen (Brady) is an awesome person. She's a great person," Pegula added. "She was texting me, 'I'm so happy, I'm so proud. This is awesome.'"

Elsewhere, fourth seed Daniil Medvedev and seventh seed Andrey Rublev both won to ensure an all-Russian quarter-final.

Medvedev, the 2019 US Open runner-up, blew away American world number 192 Mackenzie McDonald 6-4, 6-2, 6-3 to extend his winning streak to 18 matches.

Rublev, who is also unbeaten this year, went through when Norway's Casper Ruud retired after losing the first two sets.

The 22-year-old Norwegian had reached the last 16 at a Slam for the first time -- emulating his father, Christian, who achieved the same feat at the 1997 Australian Open.

With qualifier Aslan Karatsev already through to face Grigor Dimitrov in the top half of the draw, it means there will be three Russian men in the last eight of a Slam for the first time since the Open era began in 1968.