The 25-year-old Scot will now face world No. 1 Djokovic in Sunday's final in a rematch of last year's Australian Open semi-final epic that lasted almost five hours with the Serb ending up prevailing 6-3, 3-6, 6-7, 6-1, 7-5.
However, since then Murray won the Olympics title at Wimbledon in London and then won his first Grand Slam title at the US Open where he beat Djokovic, so now has confidence of getting over the line on the biggest of stages.
If Murray is able to win the final, he will become the first player ever to win two straight Grand Slam titles with the first two major wins of his career.
Djokovic will have had an extra day to recover than Murray, though, and even though he had tough matches during the two weeks against the likes of Stanislas Wawrinka and Tomas Berdych, he cruised in his semi-final beating Spain's David Ferrer 6-2, 6-2, 6-1 in just 89 minutes.
Murray did outplay Federer in the semi-final and the Swiss master who has 17 Grand Slams to his credit was playing catch up virtually all night.
Murray hit 25 aces to Federer's five, and even more impressively didn’t have one double-fault. He hit 62 winners to Federer's 43 as well, and had just 47 unforced errors to Federer's 60 as he won 177 points in total to 151 to book his deserved place in the final.
Murray dropped serve for the first time early in the fourth set, but broke back and then looked poised to quickly finish Federer off when he broke again, to love, for a 6-5 lead.
But after the Scot went up 30-15 to be two points from victory, Federer reeled off the next three to force a tiebreaker, then stormed through that to level the match.
As in the third set, Murray channelled frustration into renewed venom, speeding through the first three games of the fifth. This time there was no let-off for Federer as Murray kept his foot down all the way to the finish.
Murray has had a largely dominant performance the whole two weeks to make the final not losing a set against Robin Haase, Joao Sousa, Ricardas Berankis, Gilles Simon and Jeremy Chardy.
The final now between Djokovic and Murray will be the 18th meeting between the pair of 25-year-old's who are at the peak of their games, and remarkably have just seven days that separate their birthdays.
Djokovic leads the head-to-head series 10-7 including the last two of 2012 following Murray's breakthrough US Open triumph where he beat the Serb 7-6, 7-5, 2-6, 3-6, 6-2 in the final for his first Grand Slam title.