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Murray shouted "wake up!" during one of many frustrating moments on Rod Laver Arena but a dozy display proved sufficient as the Scot sealed a 7-5 7-6 (7/5) 6-2 victory.
He will now face Russian teenager Andrey Rublev, the world number 152 who had earlier registered a surprise win over Yen-Hsun Lu.
Murray, walking out on court at just after 3pm local time, was not addressed as 'Sir' in the announcer's introduction but that will have been of little concern to the top seed, who insisted in his post-match interview that "Andy is definitely fine". Instead, the Briton is likely keen to continue where he left off last season as he chases his first title in Melbourne, where he has reached the final five times but never been crowned champion.