The Swiss was handed his first significant test of the tournament against Jo-Wilfried Tsonga but came through 7-6 (7/4) 4-6 7-6 (7/4) 3-6 6-3.
He will now meet Murray, who continued his untroubled route through the draw with a straightforward win over Jeremy Chardy, in a repeat of last year's Wimbledon and Olympic finals.
"It was tough the whole match. Any set could have gone either way," Federer said.
"It was tough because you never know what Jo-Wilfried is going to come up with. I feel a bit lucky to come through."
As for playing Murray on Friday, the 31-year-old added: "I've got to recover a little but I'm going to be fine - I'm young, I recover quick.
"I'm looking forward to the match. It's going to be tough. He had a great year last year, winning his first grand slam and Olympic gold.
"He is a great guy and a great player."
Federer started in commanding fashion with a break in the opening game but was then broken himself for the first time this year.
The world number two set up a chance to move 5-4 ahead with a wonderful high baseline drive in reply to a Tsonga smash but then wasted the break-point opportunity with a sloppy forehand.
Tsonga managed to keep it on serve but could do little in the tie-break as Federer upped his game to take it 7-4.
The second was also closely fought but it went the way of the seventh seed thanks to a solitary break in game seven.
A match which had yet to scale real heights was warming up and the third went to another breaker.
And it was Federer who again came through, a mini-break handing him two set points and he took the first after some wonderful scrambling defence forced his opponent to push a low backhand volley wide.
The 17-time major winner appeared to be going in for the kill when he claimed four break points early in the fourth but Tsonga held on, aided by some big serving and heavy groundstrokes.
The 2008 Melbourne runner-up was also having more joy on the Federer serve and he established a 4-2 lead when Federer pushed a routine forehand beyond the baseline.
The players then traded breaks as nerves started to become a factor before Tsonga held firm to serve it out and take it to a deciding set.
Having been so close for so long, the fifth was slightly anti-climactic as Federer dominated.
He cruised into a 4-1 lead and wasted two chances to claim a double-break, Federer setting up the point only to miss the easy drive volley into the open court.
Tsonga held and then staved off four match points in his next service game but it was merely delaying the inevitable as Federer got the job done to go through in three hours and 34 minutes.
Murray is confident he will have little problem in stepping up his performance level for the clash with Federer, despite his low-key passage to the last four.
The Scot has barely broken sweat in advancing to his fourth successive Melbourne semi - although he turned in a much-improved display against big-hitting Chardy.
He accepts, though, that he will need to play better still against the Swiss with a place in Sunday's final at stake.
"I think you have to trust yourself that when you are tested you're going to play better tennis," he said.
"You never know for sure but in the build-up to the tournament I played very well.
"I haven't lost a set here yet so maybe I am expecting to play too well. But I've done a good job so far in this tournament.
"I can't be disappointed with where my game's at and I hope in the next round I play better again."
Having come through a flat, lifeless contest against a fatigued Gilles Simon on Monday, the encounter with Chardy was, at least, competitive.
But Murray was never seriously threatened by the world number 36 and came through 6-4 6-1 6-2 in one hour and 51 minutes.