The Russian fifth seed won 6-1 6-7 (5-7) 6-0 under the Rod Laver Arena roof, as rain halted play on outside courts.
Twelfth seed Belinda Bencic and men's seventh seed Kei Nishikori progressed.
Roger Federer takes on Grigor Dimitrov later on Friday, with Novak Djokovic and Serena Williams featuring in the night session at Melbourne Park.
Switzerland's Bencic beat Kateryna Bondarenko of Ukraine 4-6 6-2 6-4, while Nishikori saw off Spain's Guillermo Garcia-Lopez 7-5 2-6 6-3 6-4 despite requiring treatment on his wrist.
"It was a little bit sore in the beginning, but after the treatment it was fine," said the Japanese player.
French ninth seed Jo-Wilfried Tsonga won in three tight sets against compatriot Pierre-Hugues Herbert, 6-4 7-6 (9-7) 7-6 (7-4). Read more on bbc.