The elegant 17-time Grand Slam winner defeated the Wimbledon champion 6-3 6-4 6-7 (6-8) 6-3 in the Rod Laver Arena and will face familiar foe Rafael Nadal in the last four.
Murray broke back when Federer was serving for the match and saved two match points in the tie-break, before finally summoning the spell to end Federer's sorcery and take the third set.
However Federer regained control in the fourth and broke the Scot in the penultimate game of the set, before serving out the match.
Nadal earlier struggled past Grigor Dimitrov in four sets, despite nursing a blister on his left hand.
Federer's victory also sets up the prospect of an all-Swiss final against Novak Djokovic's conqueror, Stanislas Wawrinka. He will take on the Czech Republic's Tomas Berdych.
Currently coached by seven-time Slam winner Stefan Edberg, Federer has not won a major since his defeat of Murray in the 2012 Wimbledon final.
His 21st meeting with Murray was the first time Federer was the lower ranked, and despite Murray's lack of matches this will rank as one of Federer's outstanding displays in the twilight of his career.