Murray, the third-ranked player in the world, appeared to be the more confident player throughout a 6-4, 6-7 (5-7), 6-3, 6-7 (2-7), 6-2 victory over Federer. He heads into the men's singles final Sunday against world No. 1 and two-time defending Australian Open champion Novak Djokovic.
Djokovic beat Murray in the 2011 finals in Melbourne but Murray picked up his first Grand Slam title at the 2012 U.S. Open with a five-set win over Djokovic. Djokovic is 10-7 all-time against Murray.
Djokovic will be well-rested. Since a 5-hour marathon in the quarterfinals, he had relatively quick matches, including an 89-minute, straight win Thursday over fourth-seeded David Ferrer in the semifinals.
Murray and Federer, who met for the 2010 Australian Open title, played for 4 hours Friday before Murray finished things off with his sixth break of the match.
Even with Murray seemingly playing better than Federer, Federer broke Murray at 6-5 of the fourth set and extended the match. But Murray had a second-game break in the fifth set and dropped just one point in three service games in getting to 5-2 of the final set.
In addition to the six dropped service games, Federer had an uncharacteristic 60 unforced errors against 43 winners. He only forced six break points on Murray, who won 71 percent of the points on serve.
Federer, playing in his 10th consecutive Australian Open semifinal, had trouble getting ahead of Murray, who used a third-game break in the first set to take an early lead.
Federer did win the second set, holding on in the tiebreaker after a building 4-1 lead. That was the first set Murray has lost in the tournament. Murray's sixth-game break proved to be the difference in the third set as he used one of his 21 aces on the day to finish off the set.
Federer had a break -- one of his two of the match -- for a 4-1 lead in the fourth set only to have Murray answer in the seventh game. Murray pulled to the verge of the of a title berth with an 11th-game break at love but Federer answered with a break the next game and forced the tiebreaker, which he controlled.