By Alastair Himmer
The Briton, beaten by Roger Federer in last year's Melbourne final, produced arguably the best tennis of the tournament so far to see off Melzer in an hour and 44 minutes.
"I hit the ball the best I have done of the first few matches," fifth seed Murray told reporters while munching on a bar of chocolate.
"The matches are going to get tougher. I'm ready for that mentally. I'm not expecting to go through the tournament winning matches like that."
Murray was cheered on from the players' box by popular Scottish comedian and actor Billy Connolly.
"We used to drive from Scotland down to England for tournaments and listen to him on cassettes," said Murray with a smile.
"My mum and dad were pretty lenient with that stuff," he added, referring to the comic's often colorful turn of phrase.
"Probably why my language is so bad on the court!"
Murray had Melzer turning the air blue himself, the 11th seed furiously hurling his racket to the court as the Scot powered into a two-set lead.
He next plays Ukrainian Alexandr Dolgopolov, who earlier upset fourth seed Robin Soderling.
"It will be difficult," said Murray. "He's a very strange guy to play against -- very funky style."
Melzer, who will rise into the world's top 10 for the first time when the next rankings are published, cursed his luck for running into a player in such devastating form.
"You have to give him credit for how well he played," said the 29-year-old. "I think the first set he made one unforced error.
"He plays extremely intelligently. It was an extraordinary effort from him."
(Editing by John O'Brien)