No. 2-ranked Murray had a 4-6, 7-5, 6-7 (4), 6-4, 6-2 win over No. 13-seeded Milos Raonic in a momentum-swinging match that finished just before midnight.Murray, who has lost all four previous finals he has contested at Melbourne Park, will be facing five-time champion Novak Djokovic, who has never lost a title match on Rod Laver Arena.
Three of Djokovic's wins in Australia have come in finals against his old friend Murray, every odd-numbered year since 2011.
Murray has had a lot on his mind this time, too. His wife, Kim, is back in Britain and due to have their first baby next month. Kim's father, Nigel Sears, was in Melbourne as coach for Ana Ivanovic and had to be rushed to a hospital by ambulance during one of her matches on Rod Laver Arena, which happened to be coinciding with Murray's fourth-round match on an adjacent arena.
Sears spent a night in hospital, with Murray visiting, and was considered well enough to return home, giving Murray at least one less reason to be distracted.
He had a lot on his mind Friday against Raonic, who was playing in only his second Grand Slam semifinal, and aiming to be the first Canadian man to reach the final of a major. He started well and twice had leads, but seemed to be hampered by an upper right leg injury from late in the fourth set, restricting his serve-and-volley game.
Murray said he sensed Raonic slowing down, but had to keep his mind on his own side of the court.
He'll have to do that again on Sunday night against Djokovic, who won 27 of his 28 matches in Grand Slams in 2015 — his only loss coming in the French Open final.
"I need to keep my game plan very well, not have any lapses in concentration and just play the best I can," said Murray, who has won just nine of his 30 career meetings with Djokovic. "He loves playing on this court, we've played a bunch of times here. Hopefully it can be a different result."
Murray's older brother Jamie is in the doubles final on Saturday, giving the Scottish siblings the distinction of being the first brothers to appear in the singles and doubles finals at the same major in the Open era. The men's doubles decider follows the women's final between six-time champion Serena Williams and No. 7-seeded Angelique Kerber.
Jamie Murray will combine with Bruno Soares in the men's doubles title match against Daniel Nestor and Radek Stepanek.
In the earlier women's doubles final, the No. 1-ranked team of Martina Hingis and Sania Mirza beat the Czech pair of Andrea Hlavackova and Lucie Hradecka 7-6 (1), 6-3 to extend their winning streak to 36 matches on the way to a third Grand Slam title together.
Hingis and Mirza won the Wimbledon and U.S. Open titles last year.
Mirza couldn't extend her run in mixed doubles, losing with her partner Ivan Dodig of Croatia 7-5, 7-6 (4) to Elena Vesnina and Soares in the semifinals later Friday. Vesnina and Soares will play American Coco Vandeweghe and Horia Tecau of Romania in Sunday's final.