Third seed Alexander Zverev continued his quest for a maiden Grand Slam title with a 6-3 6-4 6-4 win over Moldovan qualifier Radu Albot. Up next for the Tokyo Olympics champion is Denis Shapovalov, who he has beaten four times in six meetings.
Seventh seed Matteo Berrettini staved off a strong challenge from 18-year-old Carlos Alcaraz to win a huge centre court battle 6-2 7-6(3) 4-6 2-6 7-6(10-5) and reach the fourth round for the second time, equalling his best Australian Open result.
Berrettini rolled his ankle and crashed to the ground while up 1-0 in the decider but soldiered on after a medical timeout and closed out the victory when Alcaraz double faulted in the super tiebreak.
Denis Shapovalov, the 14th seed, sealed a 7-6(4) 4-6 6-3 6-4 victory over Reilly Opelka to make the fourth round at Melbourne Park for the first time in his career.
Earlier, 2016 quarter-finalist Gael Monfils moved past 16th seed Cristian Garin 7-6(4) 6-1 6-3 while Miomir Kecmanovic also advanced with a 6-4 6-7(8) 6-2 7-5 win over Lorenzo Sonego.
Madison Keys came from a set down to claim a 4-6 6-3 7-6(10-2) win over China's Wang Qiang to book her place in the fourth round. The American, a former semi-finalist at Melbourne Park, plays eighth seed Paula Badosa next.
Eighth seed Paula Badosa, who emerged as a contender for a maiden Grand Slam title after winning the Sydney Tennis Classic last week, edged past Marta Kostyuk 6-2 5-7 6-4 to reach the fourth round at Melbourne Park for the first time.
“She played top-five level tennis. I had to give it my all. She is going to be one of the best players soon,” said Badosa.
A determined Barbora Krejcikova fought back from a set and a break down to overcome Jelena Ostapenko 2-6 6-4 6-4 in a battle between former French Open champions on Rod Laver Arena.
“Today’s match was very tough, I had to dig deep to get this win, so I’m very happy and proud of myself. I’m never going to leave without a fight and I’m happy to show that on the court,” Krejcikova said.
Krejcikova returned from an eight-minute bathroom break - which she blamed on a broken necklace - and shrugged off a time violation ahead of the decider to secure the victory. Up next for the fourth seed is Victoria Azarenka.
Last year’s quarter-finalist Jessica Pegula shook off a slow start to get past Nuria Parrizas Diaz 7-6(3) 6-2 and reach the fourth round, where the American will face fifth seed Maria Sakkari, who beat an ailing Veronika Kudermetova 6-4 6-1.
Men’s third-round results
(6) Rafael Nadal (Esp) bt (28) Karen Khachanov (Rus) 6-3 6-2 3-6 6-1, (7) Matteo Berrettini (Ita) bt (31) Carlos Alcaraz Garfia (Esp) 6-2 7-6 (7-3) 4-6 2-6 7-6 (10-5), (19) Pablo Carreno-Busta (Esp) bt Sebastian Korda (USA) 6-4 7-5 6-7 (6-8) 6-3, (3) Alexander Zverev (Ger) bt Radu Albot (Mol) 6-3 6-4 6-4, (14) Denis Shapovalov (Can) bt (23) Reilly Opelka (USA) 7-6 (7-4) 4-6 6-3 6-4, Miomir Kecmanovic (Ser) bt (25) Lorenzo Sonego (Ita) 6-4 6-7 (8-10) 6-2 7-5, (17) Gael Monfils (Fra) bt (16) Christian Garin (Chi) 7-6 (7-4) 6-1 6-3, Adrian Mannarino (Fra) bt (18) Aslan Karatsev (Rus) 7-6 (7-4) 6-7 (4-7) 7-5 6-4
Women’s third-round results
(8) Paula Badosa Gibert (Esp) bt Marta Kostyuk (Ukr) 6-2 5-7 6-4, (21) Jessica Pegula (USA) bt Nuria Parrizas-Diaz (Esp) 7-6 (7-3) 6-2, (24) Victoria Azarenka (Blr) bt (15) Elina Svitolina (Ukr) 6-0 6-2, Amanda Anisimova (USA) bt (13) Naomi Osaka (Jpn) 4-6 6-3 7-6 (10-5), (1) Ashleigh Barty (Aus) bt (30) Camila Giorgi (Ita) 6-2 6-3, (4) Barbora Krejcikova (Cze) bt (26) Jelena Ostapenko (Lat) 2-6 6-4 6-4, Madison Keys (USA) bt Qiang Wang (Chn) 4-6 6-3 7-6 (10-2), (5) Maria Sakkari (Gre) bt (28) Veronika Kudermetova (Rus) 6-4 6-1