The 28-year-old dominated throughout against the former junior world number one to secure a 6-1 6-2 6-3 win in hot conditions in Melbourne.
“It got tough at the end and there were a lot of long games and rallies. Alex fought hard and made it very competitive,” said Murray.
“It was hot so I was glad to get it done in three sets.”
Murray also said that there was no news from his pregnant wife Kim, who is not due to give birth until February.
The Scot, who will now face Australian Sam Groth in round two, has said that he will leave the tournament if she goes into labour.
“I don’t have any news because I’ve just come off the court,” he added.
“I’m hoping my phone hasn’t been buzzing in my bag but Kim will message the team if anything happens in any of the matches.”
Fellow Brit Dan Evans lost 6-1 6-0 6-4 to Spain’s Feliciano Lopez, while Aljaz Beden was beaten by Steve Johnson 6-3 6-4 7-6 (7-3).
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