In a rollercoaster match lasting nearly five hours the Serbian top seed, trailing two sets to one, stormed back to win 6-3, 3-6, 6-7 (4/7), 6-1, 7-5 to set up a title match with Rafael Nadal.
“There’s not any words that can describe the feeling I have now,” Djokovic said. “Andy deserves the credit to come back into the match after 2-5 down. He was fighting, I was fighting.”
Djokovic now gets a shot at his third Australian Open title while Murray’s quest for Britain’s first male grand slam title in 76 years goes on.
Djokovic, who enjoyed a stellar season in 2011, winning 10 titles including the Australian Open, Wimbledon and the US Open, drew first blood on Rod Laver Arena, breaking in the fourth game when the Scot double-faulted.
He took the opening set and broke again early in the second but Murray cut out the errors and began to dictate the points, levelling the match and taking the third set on a tie-break.
But there was a sudden momentum shift at the start of the fourth set as errors crept back into Murray’s game and Djokovic raced through the gears to take it 6-1 in just 25 minutes.
He made a crucial break in the sixth game of the final set and although Murray broke back, he won the match by breaking the Scot in the 12th game.
“It was one of the best matches I’ve played, but emotionally and mentally it was hard,” Djokovic said. “I felt like we were breaking each other’s serves easier than serving it out.”
After Djokovic broke in the first set Murray broke back with a powerful backhand winner down the line, but the fourth seed was immediately under pressure on his own serve, broken to love as Djokovic took take the first set.
Djokovic broke Murray for the third time in the match at the start of the second set as the Scot struggled to gain a foothold in the match.
But in a statement of intent Murray, an Australian Open finalist in 2010 and 2011, produced a leaping overhead at the start of game four and stepped up a gear, levelling the set at 2-2.
It proved a turning point as the fired-up Scot found his best form, holding easily and then breaking again as he turned the screw in only the second grand slam meeting between the two players.
However, Djokovic broke Murray’s sequence of four straight games with a break of his own to stay alive.
He looked set to deny the Scot when he earned two break points as Murray served for the set at 5-3, but Murray stayed strong to level the match.
Murray stayed in charge in a gruelling third set lasting 88 minutes, dictating the points with the Serb struggling to hold serve. Djokovic looked up to the heavens and crossed himself when he served a rare ace.
But Murray could not make his dominance count and was forced to dig deep to save three set points, levelling the set at 5-5 as the clocked ticked onto three hours. The set went to a tie-break which Murray took to move ahead.
Djokovic, who enjoyed one of the greatest seasons in tennis history in 2011, is bidding become just the fifth man to win three consecutive grand slam titles in the open era when he faces Nadal on Sunday.
“I’m going to try to recover but obviously it’s going to be physical as well, so I need to do some push-ups tonight,” he said.