World number one Djokovic will face second seed Rafael Nadal in Sunday’s final, after the Spaniard beat Roger Federer in the first semi-final.
Having looked beaten at two sets to one, the defending champion capitalised on a poor fourth set from Murray, before also surviving a final set fightback from the Brit who found himself 5-2 down.
But in the end the four-times Grand Slam champion had too much for Murray and sealed victory after four hours and 50 minutes; collapsing on to the court when Murray hit a running forehand into the net.
Djokovic began the match in much the same way he had finished against fifth seed David Ferrer, sucking in the air as if he was struggling to breathe. Nevertheless, he was still the one to make the better start, breaking in the fourth game when Murray slapped down his first double fault of the night.
The Brit bounced straight back with a break of his own, courtesy of a blistering cross court forehand winner, but he could not contain the rampaging Serb for long, Djokovic once again taking the lead in the sixth game when Murray dumped a routine backhand into the net.
Djokovic wrapped up the first set before putting the Brit under even more pressure with a break in the opening game of the second.
But the Scot, perhaps inspired by a glare from his new coach Ivan Lendl, suddenly found some attacking momentum; quickly holding before going on to break back in the fourth game with successive smash winners doing the damage before Djokovic hit long.
Murray broke again two games later, this time letting his forehand do the damage, to take the lead with his fourth straight game before handing it back to Djokovic with another sloppy game.
However, unlike the first set, it was only a temporary blip from the Brit as he once again broke the Serb’s serve before serving out the set with a huge serve out wide that Djokovic could only return into the net.
Murray’s inability to back up a break of serve with a solid service hold dogged him throughout the match, a lead in the third set, when Djokovic looked to be physically and emotionally close to quitting, twice being squandered when he conceded an immediate break back.
The Brit managed to lift his game in the inevitable tie-break and he took a step closer to the final by winning the breaker 7-4 with a huge serve across court.
But once again he could not make his advantage tell, as Djokovic stormed back into contention with breaks in the first, third and seventh games of a shockingly poor fourth set from Murray to level up at two sets all and push the match to a decider.
Suddenly the world number one had all the momentum, and secured the lead in the sixth game with a blistering cross court forehand winner.
A quick hold of serve left a visible exhausted Murray serving to stay in the match at 5-2, only for the Brit to hold with ease before going on to break back, with a stunning cross court forehand passing shot, and level up with another hold.
Murray even enjoyed more break points in the 11th game, standing on the brink of an amazing comeback to book his place in a third straight Australian Open final.
But the fourth seed could not take advantage of any of his three chances as Djokovic summoned up his last reserves of energy to produce some incredible defence and somehow hold on for a 6-5 lead.
It was the last throw of the dice from Murray, who clearly had nothing left for his own service game; the Brit putting a backhand into the net to hand Djokovic two match points.
Only one was needed for the Serb however, as Murray put a defensive forehand into the net to hand Djokovic a chance to face world number two Nadal in a third straight Grand Slam final.