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.
Azarenka needs Australia win to stay No. 1
Azarenka defeated Maria Sharapova in the 2012 Australian Open women's final for her first Grand Slam title. It also moved her into the No. 1 world ranking for the first time.
She's held that position for most of the ensuing year but the surge by Serena Williams over the second half of 2012 -- including a win over Azarenka in the U.S. Open final -- leaves Azarenka needing a win Saturday over Li to retain the title and top ranking.
Saturday will mark the third major tournament final for Azarenka.
Li is also in her third Grand Slam final. She was lost 2011 Australian Open final to Kim Clijsters but beat Francesca Schiavone for the 2011 French Open championship. She's only been in one other major tournament semifinal.
Azarenka's run to the finals was surprisingly clean. She faced just one seeded player and that was No. 29 Sloane Stephens in the semifinals. Azarenka has lost one set in the tournament.
Li, on the other hand, drew four seeded players, including fourth-ranked Agnieszka Radwanska, who hadn't lost in 2013, and second-seeded Maria Sharapova, who'd dropped only nine games in her first five Australian Open matches. Li defeated both in straight sets.
Azarenka has won her last four matches against Li, running her career record to 5-4. Two of the three matches, however, went three sets.
Venus Williams has back injury
PARIS, Jan. 25 (UPI) -- Venus Williams has withdrawn from a tournament in Paris and the upcoming Fed Cup quarterfinals due to a back injury, tournament organizers said Friday.
Organizers said Williams informed them she will miss next week's Open GDF Suez tournament in Paris.
Williams also said she will sit out the United States' Fed Cup series in Italy. The Fed Cup 2013 series begins Feb. 9.
Williams, ranked No. 26 in the world, was beaten in the third round of the Australian Open by No. 2-ranked Maria Sharapova.
Her play in recent years has been limited by a series of health issues, including Sjogren's syndrome, an autoimmune disease.
Chris Wood ahead at Qatar Masters
DOHA, Qatar, Jan. 25 (UPI) -- Chris Wood shot an 8-under-par 64 Friday and built a three-stroke lead going into the final round of the European Tour's Commercial Bank Qatar Masters.
Wood had an eagle at the par-5, 548-yard 10th hole and seven birdies --six on par 4s -- against one bogey in moving to 15-under 201 after 54 holes.
Wood had five birdies in his first eight holes Friday then had an 8-foot putt for his eagle at No. 10. He had a bogey at the 12th but pulled clear with birdies at Nos. 14 and 16.
Sergio Garcia, one of the four second-round co-leaders, suffered two late bogeys in a 2-under 70 and slipped into a tie for fifth with Branden Grace (67).
The other co-leaders had worse rounds Friday with Marcus Fraser, despite three consecutive birdies in one stretch, shooting 1-under 71. He is tied for seventh. Martin Kaymer, with two birdies and two bogeys Friday, is among those tied for 11th, six strokes behind Wood.
Ricardo Santos, who led after the first round and was tied after Thursday's play, had two double bogeys and four bogeys in a 4-over 76 and dropped into a tie for 38th at 5-under for the tournament.