Roger Federer dropped another set but recovered well to defeat Marton Fucsovics in four while Novak Djokovic eased to victory over Diego Schwartzman.
World number one Ashleigh Barty survived a scare on Australia Day to set up a rematch of last year's quarter-final against Petra Kvitova.
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All Greek to Petra
Melbourne's big Greek population have turned out in force again this tournament to support Stefanos Tsitsipas and Maria Sakkari. Both are now out of the tournament, with Sakkari beaten by Kvitova on Sunday.
Several Greek fans were thrown out of Melbourne Park earlier in the tournament for rowdy behaviour, and Kvitova said: "When I was shaking hands with the umpire, I told him it was like a soccer match today. It's nice on one side. On the other side, it's tennis, and it's not Fed Cup."
Jamie Murray is a laid-back sort but it took a full 10 minutes to resolve a dispute involving a Hawk-Eye challenge during his first-round match in the mixed doubles alongside American Bethanie Mattek-Sands.
Murray was furious when the umpire did not allow him to challenge a line call as Mattek-Sands hit a shot. The supervisor was called and agreed with Murray, which did not go down well with opponent Barbora Strycova, who confronted the Scot.
The afternoon ended happily for Murray and Mattek-Sands, though, as they battled to a 3-6 6-4 10-7 victory over top seeds Strycova and Marcelo Melo.
Women: Alison Riske (18), Maria Sakkari (22), Wang Qiang (27)
Men: Fabio Fognini (12), Diego Schwartzman (14)
Who's up next?
Monday's main event comes in the first match of the night session, when world number one Rafael Nadal faces Nick Kyrgios.
Wimbledon champion Simona Halep kicks off the schedule against Elise Mertens, while a resurgent Garbine Muguruza will look to take down another top-10 player when she faces ninth seed Kiki Bertens.
Andrey Rublev takes a 15-match winning streak into his clash with Alexander Zverev and Gael Monfils meets fifth seed Dominic Thiem.