Nadal edged ahead of Australia's Nick Kyrgios, 6-3, 3-6, 7-6 (8-6), 7-6, (7-4), while Wawrinka defeated World No. 4, Daniil Medvedev, 6-2, 2-6, 4-6, 7-6 (7-2), 6-2.
They join Novak Djokovic and Roger Federer in the final eight, with the business end of the tournament rapidly approaching, reports Xinhua news agency.
Moving through in the women's draw was Simona Halep who beat Elise Mertens from Belgium, 6-4, 6-4, while an in-form Garbine Muguruza defeated ninth seeded Kiki Bertens, 6-3, 6-3, to join the quarterfinalists.
Monday night's Kyrgios-Nadal match-up was a big occasion for Aussie fans, throwing their support behind the local hopeful, who lived up to their expectations, despite it not proving to be enough.
In the past, Nadal has been critical of Kyrgios' on-court antics, which last year earned him a six-month probation from the ATP tour. However, on the night, the Australian let his tennis speak for itself, drawing praise from across the net.
"Today, I think he played very serious, he played very focused, and he tried his best," Nadal said after the match.
"When he's able to play like this, his talent is to be one of the best players in the world."
Before the match, Kyrgios emerged from the locker rooms wearing an L.A. Lakers jersey, in tribute to Kobe Bryant, who died tragically in a helicopter crash the day before. He joined a raft of other players at the tournament who paid their respects to the fallen basketball legend throughout the day.
Nadal claimed the first set, outplaying Kyrgios in most measures, hitting more winners, and forcing more errors from his young opponent.
In the past, the Australian's biggest enemy has been himself, with his game deteriorating when the score is not in his favour.
However whether it was the support of the home crowd or something else, this time after losing the first set, rather than crumble, Kyrgios stepped up to claim the second.
In a tiebreak for the third set, a glimpse of the old Kyrgios emerged, smashing a racquet, and dropping two points to give Nadal the upperhand.
Ultimately Nadal secured the match but not before Kyrgios managed to force a final tiebreak, keeping the match and the excitement alive a little bit longer for fans.
Earlier, Wawrinka and Medvedev played a thrilling match of their own, with the Swiss three-time Grand Slam champion managing an incredible resurgence from two sets down.
"When I enter the court, I enter to win. I know I have what it takes to do it. I knew it will be a really tough battle because he's a strong player," Wawrinka said after the match.
Although, two knee surgeries in 2017 threatened to put an end to Wawrinka's career, his performance at this year's Australian open suggests his old stellar form may be re-emerging.
"I think last time I played so well was before the surgery. I think for sure, I feel since the off-season my level is really high," Wawrinka said.
( With inputs from IANS )