After Rafael Nadal battled through an unexpectedly tough quarter-final with Bulgaria's Grigor Dimitrov, Roger Federer showed both his vintage best and his fallibility in beating Murray 6-3, 6-4, 6-7 (6/8), 6-3.
The Swiss great was electric in the first two sets but he tightened as he neared the finishing line, and was broken when serving for the win before passing up two match points in the third-set tiebreaker.
However, he extended Murray in a 19-minute hold at the start of the fourth set, then got the crucial break for 5-3 and, after setting up a third match point, he grabbed the opportunity with an ace.
"I thought Andy did well, he kept the ball in play and put the pressure on me and unfortunately I couldn't get it done in the third set, with either the serve or the forehand missing. So I am happy to get the win in four," Roger Federer said.
"I am much higher than I was last year and that's very satisfying just because I have confidence in my movement."
Roger Federer, in his 11th consecutive Australian Open semi-final, will face the man who has become his Grand Slam nemesis, winning their last five encounters at major tournaments.
But a day after Novak Djokovic's three-year Melbourne reign was halted by Stanislas Wawrinka, Rafael Nadal also flirted with disaster before getting out of jail against rising Bulgarian Grigor Dimitrov.
The 13-time Grand Slam champion, troubled by a huge blister on his racquet hand, went a set down against the exciting young prospect and, facing set points in the third, he was tottering.
But Dimitrov, 22, went just long on the first set point and Rafael Nadal saved another before the Bulgarian gave him a one-set lead when, gifted an easy winner off a net cord, he ballooned his forehand out.
"I was so lucky," admitted the Spaniard, who ran out a 3-6, 7-6 (7/3), 7-6 (9/7), 6-2 winner to set up a meeting with Roger Federer in his 22nd Grand Slam semi-final.
Djokovic's defeat by Wawrinka, who will play Tomas Berdych in the other semi, ensures that one of them will be able to challenge either Rafael Nadal or Roger Federer for their maiden Grand Slam title.
"I'm a bit shattered," said Dimitrov, after his title hopes slipped away. "It's tough losing that match, my first (Grand Slam) quarter-final. I came out expecting nothing less than to win."
The women's contest has been even more up-ended and there was an air of resignation rather than shock when Azarenka tamely followed Serena Williams and Maria Sharapova out of the tournament.
The Belarusian world number two was unbeaten in two years at Melbourne Park but she was comprehensively dismantled by an inspired Agnieszka Radwanska 6-1, 5-7, 6-0.
"I'll be fine tomorrow. I'll be working tomorrow. It's not the end of the world. But I'm not happy with what I did today," said Azarenka.
It ends a sometimes unhappy run of 18 wins at the tournament for Azarenka, whose loud grunting and perceived gamesmanship has earned her critics as well as fans in Melbourne.
But it was a major scalp for Radwanska, who had lost all seven previous meetings with the Belarusian, and now goes into a semi-final with Slovak 20th seed Dominika Cibulkova.
"It's hard to play someone I lost (to) so many times before. I knew she's a great player. Especially here, she was playing amazing tennis," said Radwanska.
The upset also ensures the tournament will have a new women's champion with none of the semi-finalists Radwanska, Cibulkova, Li Na and Eugenie Bouchard -- having won before.
Cibulkova reached only her second Slam semi-final when she also won against a favoured opponent in fast-rising Romanian Simona Halep.
Halep is set to break the top 10 in next week's new rankings, but she froze in her first Grand Slam quarter-final as the energetic Cibulkova dominated 6-3, 6-0 in one hour exactly.