A trouble-free 7-6, 6-4, 6-2 victory over Feliciano Lopez of Spain took him safely into round four and having not dropped a set, things could barely have gone better.
Tomorrow, he takes on 33-year-old Frenchman Stephane Robert, at No 119 the lowest-ranked player remaining in the event, and it would be a major surprise if he does not find himself in the quarter-finals of the first Grand Slam of the year.
"Today was a big step up for me," he said. "Feliciano is a top 30 player and a tricky opponent to play. I know I have a good record against him, but it doesn't change the fact he's not an easy guy to play against. He's a very different type of opponent to what you normally face. So it was a good test for me and I did well."
Dropping serve in the opening game was not the start he would have hoped for but he hit back immediately and once he had taken the first-set tie-break 7-2, there seemed little chance that Lopez would come back to beat Murray for the first time in what was their eighth meeting.
Three weeks into his comeback after four months out following back surgery, Murray is moving well and apparently playing without pain, but he was keen yesterday to play down expectations that he could go all the way to the title.
"I'm not expecting too much of myself but obviously with each round that goes by, I'm starting to feel more comfortable on the court and the body is going to adjust to playing matches again," he said. "I don't know how far I can go, but I'm doing OK so far."
On paper, Murray should be far too strong for Robert, who only got into the main draw as a lucky loser when Germany's Philipp Kohlschreiber pulled out on the eve of the tournament.
The Frenchman has spent most of his career on the second rung of the ladder, the Challenger Tour, occasionally spending nights in hostels to save money. Win or lose tomorrow, he is guaranteed the biggest cheque of his career and his relatively carefree life contrasts with that of Murray, whose ultra-professionalism has been a major part of his success.
But Murray did surprise people a little yesterday when he revealed that he had been to the casino in Melbourne a couple of times, albeit before the tournament started.
"Once the tournament starts, I like to be in my bed as soon as I can," he said. "So I stay away from that sort of stuff.
"A lot of the players go to the casino. You'll see a lot of them playing. A lot of the Americans used to go to the casino during the event. I think Marcelo Rios [the former world No 1], when he played here, there were rumours going around that he had to make the final to break even."
As the Wimbledon champion, with all that entails, Murray has no such concerns but will still be keen to save energy, particularly as his projected quarter-final will be against either Roger Federer or Jo-Wilfried Tsonga.
Four-time champion Federer has done his usual trick of waltzing through the first few rounds looking every inch the man who has won 17 Grand Slams.
His 6-2, 6-2, 6-3 win over Teymuraz Gabashvili of Russia yesterday took him into the fourth round without losing a set, the 27th time he has done that in a Grand Slam event.
But Federer's problem in the past couple of years has been that when he comes to his first tough test, he has either been found wanting or it has taken so much out of him that he is spent come the next round.
Twelve months ago, it was the latter as he edged out Tsonga in five sets in the last eight and then went down in the fifth set against Murray.
The addition of former world No 1 Stefan Edberg to Team Federer has given the Swiss a timely lift and at the age of 32, he says he is pain-free and feeling capable of big things once more.
"This is clearly a tough draw but what's important for me now is that I keep playing well and don't go crazy [worrying about]who I play now," he said. "I know Tsonga is going to be a tough opponent and it's just now up to me."
If either Murray or Federer has designs on the title, though, it seems they are going to have to get past Rafael Nadal, who was in irrepressible form last night as he thrashed Gael Monfils of France 6-1, 6-2, 6-3.
What looked a tough draw at the start of the week has turned into a cakewalk for the world No 1 and having missed last year's event because of injury, he is desperate to do well again.
He plays Kei Nishikori of Japan tomorrow but if he wins the title he would be only the second man in the Open era to win each of the four Grand Slam titles twice.
"Tonight I think I played a great match," he said. "But that's just one very good day. That makes me feel confident but I am in the fourth round, that's all."
For the first time, the last 16 of a Grand Slam also includes talented Bulgarian Grigor Dimitrov, who beat Canada's Milos Raonic 6-3, 3-6, 6-4, 7-6 and now plays Spain's Roberto Bautista-Agut.