The UK number one repeated his Olympics success against the Swiss legend, and now faces Novak Djokovic on Sunday in an attempt to win his second successive Grand Slam.
Murray was the more aggressive player from the outset with the 17-time major winner struggling to cope with his controlled, attacking play.
His victory made him the first Briton to reach three Australian Open finals after ending his grand slam hoodoo against Roger Federer.
Murray had never beaten the Swiss at a major but was a deserved 6-4 6-7 (5/7) 6-3 6-7 (2/7) 6-2 winner.
The Scot missed the chance to serve out the match in the fourth set at 6-5, but responded superbly in the decider to set up a rematch with Djokovic, who he beat to win the US Open in September.
"It's always tough against Roger," Murray said. "I think the slams are where he plays his best tennis.
"When his back was against the wall at 6-5 he played some unbelievable tennis. He missed some shots at the start of the fifth and I just stuck in there."
As for the meeting with Djokovic, who thrashed David Ferrer in Thursdsay's semi, he added: "I didn't see much of his game although I heard about it. I heard he played very well. I will have to play my best tennis to win it."
Murray and Djokovic will meet for the third time in a grand slam final at the Australian Open on Sunday.
The pair were born only a week apart in May 1987 and here we chart their path to the top.
They met for the first time at the age of 11 at a tournament in France, Murray winning easily, and it was the Scot who had a better junior career. He won the prestigious Orange Bowl aged 12 and the US Open junior title in 2004. While Murray headed to Barcelona to train as a teenager, Djokovic left Serbia at the age of 12 to work with Niki Pilic in Munich. His best performance at a junior slam was reaching the Australian Open semi-finals in 2004.
EARLY DAYS ON TOUR
Both players were quickly successful on the Futures and Challenger Tours, with Djokovic winning his first title in June 2003 in Serbia a month after his 16th birthday. Murray lifted his first senior trophy three months later in Glasgow.
FIRST GRAND SLAM APPEARANCE
Murray was given a wild card into his home grand slam at Wimbledon in 2005 and won two rounds before losing to David Nalbandian from two sets up. Djokovic also made his grand slam debut in 2005 at the Australian Open, where he lost in the first round to Marat Safin.
Djokovic was the first to break into the top 100, in July 2005, with Murray making the jump in October of the same year.
Murray was ahead of his rival in this one, winning his first ATP World Tour title in San Jose in February 2006, beating Lleyton Hewitt in the final. Djokovic followed in Amersfoort in Holland in July of the same year, defeating Chile's Nicolas Massu.
Djokovic just pipped Murray to this milestone, reaching world number 10 on March 19, 2007, four weeks before Murray achieved the same ranking.
GRAND SLAM BREAKTHROUGH
Djokovic reached his first grand slam final at the US Open in 2007, losing to Roger Federer, and won his maiden title next time out at the Australian Open in 2008. He has since added four more titles and this will be his 10th slam final. It took Murray until September 2012 to win his first title, beating Djokovic in five sets at the US Open. He reached his first final in New York in 2008 and lost four finals before winning one.
WORLD NUMBER ONE
Djokovic reached the top of the world rankings after winning his first Wimbledon title in 2011 and regained it at the end of last season. He has spent a total of 65 weeks at number one. Murray's best ranking so far is number two, which he reached in August 2009.