The Scot smashed a racket in frustration as he dropped his first set of the tournament but was still far too good for Stephane Robert, the world number 119, beating the Frenchman 6-1 6-2 6-7(6) 6-2.
Three times runner-up in Melbourne and fourth seed this year, Murray played only two competitive matches before the tournament and says he still feels under-cooked going into a last-eight clash with four-times champion Roger Federer.
"I said at the start of the tournament, I can't honestly say my expectations are as high as if I'd been playing for the last four months," Murray told reporters.
"It's been a good effort so far to get to the quarter-finals of a slam this soon after back surgery, so I'm happy with that.
"But I'm not far away from winning the event. Anyone's that's in the quarters is close. I just look forward to that match and hopefully play a good one."
Murray raced through the opening two sets against Robert, a lucky loser who was appearing in the fourth round of a grand slam for the first time.
The match looked over when Murray served for victory at 5-4 in the third set but Robert saved two match points and two more at 6-4 in the tiebreak before taking it 8-6.
Murray's frustration boiled over as he smashed his racket in anger but he shrugged off the disappointment quickly, breaking for 3-1 in the fourth and easing to victory.
"Sometimes it's necessary (to break a racket)," 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."
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."
(Editing by Ed Osmond) nL3N0KU2YG
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