Melbourne - Rafael Nadal won a grudge match with Nick Kyrgios to reach the Australian Open quarter-finals and keep the heat on Roger Federer's record for Grand Slam titles on Monday.

The world number one, labelled "super salty" by Kyrgios after he criticised the Australian's behaviour last year, fought off a furious challenge to go through 6-3, 3-6, 7-6 (8/6), 7-6 (7/4).

As the tennis world mourned the death of Kobe Bryant, Kyrgios arrived at Rod Laver Arena wearing an LA Lakers shirt, and 15-year-old Coco Gauff had tributes to the basketball great scrawled on her trainers during the doubles.

There was also controversy as Australia's Margaret Court, often criticised for her deeply conservative views, was honoured for her 1970 calendar-year Grand Slam.

Nadal and Kyrgios had been feuding after some bad-tempered matches but the Spaniard said he was impressed by what he'd seen from the often-temperamental Australian at this tournament.

Kyrgios fought back to challenge Nadal in a high-octane clash played in good spirit, with a polite handshake afterwards -- a far cry from some of their previous exchanges.

"When he is playing like today with this positive attitude he gives a lot of positive things to our sport," said the Spaniard.

"He's one of the highest talents we have on our tour and I like the Nick Kyrgios during the whole of this tournament."

The 19-time Grand Slam winner will next play Austria's Dominic Thiem -- his victim in the last two French Open finals -- as the clay king targets Federer's all-time record of 20 Major titles.

Elsewhere, powerful Swiss Stan Wawrinka beat fifth seed Daniil Medvedev 6-2, 2-6, 4-6, 7-6 (7/2), 6-2 to set up a quarter-final with Germany's Alexander Zverev, who overcame close friend Andrey Rublev 6-4, 6-4, 6-4.

And Simona Halep rose to number two in the world with a 6-4, 6-4 victory over Elise Mertens, taking a big step forward in a rapidly clearing women's draw.

The Wimbledon champion from Romania, who avoided an exodus of top seeds in the previous round, will next play Estonia's Anett Kontaveit, a 6-7 (4/7), 7-5, 7-5 winner against Iga Swiatek of Poland.

"She's strong. I'm here just to face any challenge I have. So I'm not thinking negative," Halep said of Kontaveit. "I just want to go there and to give my best."

Angelique Kerber, the 2016 champion, was the latest big name to fall as she went down to Russia's Anastasia Pavlyuchenkova 6-7 (5/7), 7-6 (7/4), 6-2.

Pavlyuchenkova's quarter-final will be against Garbine Muguruza, the two-time Grand Slam champion who is resurgent since reuniting with coach Conchita Martinez, beating Kiki Bertens 6-3, 6-3.

"It's like couples, we all want Brad Pitt and Jennifer Aniston to get back together, right?" joked Martinez, the 1994 Wimbledon champion.

Earlier, Martina Navratilova and John McEnroe were among the big names to criticise Court, the 24-time Major-winner whose 1970 sweep of the Grand Slam titles was marked with a short ceremony at Rod Laver Arena.

Navratilova said the devout Christian's deeply conservative views were "actually hurting people", while fellow American legend McEnroe called Court a "crazy aunt".

The Australian once praised South Africa's apartheid system, said "tennis is full of lesbians" and described transgender children as "the work of the devil".

"There's only one thing longer than the list of Margaret Court's achievements: it's her list of offensive and homophobic statements," McEnroe said in a video for Eurosport.

In Monday's quarter-finals, six-time champion Roger Federer will play America's Tennys Sandgren and title-holder Novak Djokovic, going for his eighth title, is against big-serving Canadian Milos Raonic.

Australia's women's world number one Ashleigh Barty plays two-time Wimbledon winner Petra Kvitova, and Tunisia's Ons Jabeur, the top-ranked player from Africa, takes on America's Sofia Kenin.