As the clock in the corner of the Rod Laver Arena ticked quarter to midnight local time, the Scot, who recovered after twisting his ankle early in the fourth set, snarled and clawed his way to a 4-6, 7-6, 3-6, 7-6, 2-6 win.
Murray had looked unshakeable in earlier rounds as opponent after opponent struggled in vein to take a set off him. But even the might of the 17-time Grand Slam winning Swiss could only force the Brit to relinquish two after tie-breaks.
"It was really tough out, I'm just glad I got through it," admitted an exhausted Murray, who will now face the unnerving task of stopping Novak Djokovic claiming a record third consecutive Aussie Open.
"Roger is a great player and I always knew it was going to be hard. It was a real test for me but I'm just delighted to be in the final."
And so he should be, as it quite easily could have slipped away from him on more than one occasion.
Murray, looking to reach his third Melbourne final, made a strong start to the match, before a combination of unforced errors and sublime play from the Swiss allowed his opponent to creep back into the match when it looked to be beyond him.
However, if the Brit's maiden major win at Flushing Meadows has taught us long-suffering Scots anything, is that Murray genuinely doesn't know when he's beaten.
And this attitude served him well as he fought his way back into the match not once but twice after seeing both tie-breaks slip away from him, something a younger Murray - or one without the guiding hand of coach Ivan Lendl - would have failed to do.
"When his back is against the wall, Roger plays some unbelievable shots," said Murray.
"I've been known for losing a few big matches. I'd never beaten Roger in a big match until the Olympics but it definitely has helped me. I didn't see much of Novak's semi but I heard he played extremely well. I think this is third Australian Open in a row and I'll need to play at my best to beat him. I'm sure that I can.
Things are beginning to look up Down Under.