The Scot went a set down before eventually taking the match 4-6 6-3 6-4 6-2.
"I remember I was in that position a few times when I was younger when there's not so much pressure on you," Murray said. "He came out and played some great tennis, he was going for his shots and hitting big. I had to really dig in the beginning of the second set to come back into it."
Speaking of the Melbourne heat, Murray said: "On this court especially it's tough. There was very little shade right until the end. There were a few long rallies and he made me do a bit of running, so I need to make sure in the next round I play a little bit closer to the base line."
Despite the early scare, Murray insists that he is confident going forward.
"You always expect tough matches. He's one of the up-and-coming guys, he's going to be a very good player," he said.
"I started to play better towards the end of the match, but you want to start playing your best tennis towards the end of the tournament if you can."
Murray is currently ranked fourth in the world.