The number four seed and three-time finalist looked to be cruising against qualifier Stéphane Robert, who made the main draw as a lucky loser, only to suddenly stutter with the finish line in sight.
He won the first two sets in double quick time but squandered two match points as his opponent rallied, Murray dropping his first set of the tournament on a tie-break.
But the British number one soon recovered, his 33-year old opponent - who had played six matches to reach the second round of a Slam for the first time in his career - seeming to struggle with an injury.
And he closed out the match 6-1, 6-2, 6-7, 6-2, holding his final service game to love and completing the win with a thundering ace.
"He's a fun player to watch but not to play against," said Murray.
"He made it very tricky for me, he's very unorthodox. You want to, if you can, close these matches out when you have the opportunity.
"I think I had three or four match points on my own serve. I tried to stay focused at the beginning of the fourth set, got an early break and that helped."
"Sometimes it's necessary (to break a racquet)," Murray said. "Losing that set was frustrating because it obviously means you're out there another 30, 40 minutes at least, when I would preferably have been in the locker room.
"My racket bit the dust. Unfortunate for it. But I was glad I managed to start well in the fourth."
It's a fifth consecutive quarter-final at the Australian Open for the Olympic and Wimbledon champion and a 12th straight last-eight appearance in all Grand Slams.
In truth Murray, in only his second tournament since returning from back surgery, has not yet been tested in Melbourne but acknowledges the tournament will now get serious with Roger Federer, who produced a masterclass of tennis to beat Jo-Wilfried Tsonga 6-3 7-5 6-4, waiting in the last eight.
However, Murray said that despite his lack of match practice, he still believed he has a chance of making the last four.
"It just depends on the day," he said. "I need to play a great match.
"If I strike the ball like I did for the first two and a half sets today, I'll give myself an opportunity in the match."
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