Murray registered a convincing 6-3 6-0 6-2 victory over the Russian player.
He will next face US player Sam Querrey.
Britain's Dan Evans, however, created a magical moment on the court when he beat seventh seed Marin Cilic 3-6 7-5 6-3 6-3.
This was a major upset in Australian Open this year.
Evans will face Bernard Tomic in the next round.
Swiss Tennis star Roger Federer advanced to the third round, where he will meet Tomas Berdych, by beating Noah Rubin 7-5, 6-3, 7-6 (3).
Image: Santabanta.com
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