The first two, serve-dominated sets were decided on tie-breaks before Djokovic claimed the first break of the match late in the third.
It proved a pivotal moment with US Open champion Murray, who was struggling with blisters on his right foot and a hamstring problem, unable to mount a fightback as Djokovic cruised through the fourth to complete a 6-7 (2/7) 7-6 (7/3) 6-3 6-2 success.
His triumph handed the Serbian a place in the history books as the first man in the Open era to win three successive Melbourne crowns.
The first two sets were similar with very few opportunities offered to the receiver.
Djokovic had the better chances in the first with five break points split between the sixth and eighth games only for Murray to serve his way out of danger.
The world number one's frustration at failing to convert, coupled with irritation with his footwear, boiled over in the tie-break as his game capitulated.
It was Murray who was the aggressor in the second as he looked to double his advantage.
He had three chances to leap into a 2-0 lead but Djokovic changed tack, charging the net to escape immediate danger.
It remained on serve until another breaker which was tight until Murray threw in just his third double fault of the tournament at 2-2.
He put his first serve into the net and was shaping up to deliver the second when he noticed a feather dropping on to the court out of the corner of his eye.
Having removed it, he promptly put the second serve long.
It was all Djokovic needed to level the match and the momentum appeared to swing further in his favour when Murray had to call a medical time-out for blisters at the change of ends with television pictures showing the extent of the damage to his right foot.
There was no immediate change in his movement although there was the definite sense the match was now Djokovic's for the taking.
And the top seed needed no second invitation as he set up three break points for a 5-3 lead.
Two poor forehands saw the first two come and go but Murray could not escape a third as Djokovic claimed the first break of the match before serving it out.
Murray was clearly upset at umpire John Blom for not doing more to quieten the crowd and in particular one heckler who had forced him to halt his service action twice at important points of the third set.
Yet he started the fourth on the front foot, setting up his first break point chance since the second game of the second set only for Djokovic to close the door with a booming serve out wide.
By now, Murray was also clutching his left hamstring and it was no surprise that Djokovic broke again for 2-1, winning a long rally at 30-40 after a tired-looking Murray jammed a backhand into the net.
The match was slipping away from Murray and he dropped his serve once more on a double fault as Djokovic established a 4-1 lead.
The effort was certainly there as the world number three continued to chase down every ball despite being in obvious discomfort but there was no let-up from Djokovic as he completed his 21st consecutive win in Melbourne and gained revenge for his defeat to Murray in the US Open final last September.
Murray praised the champion in the post-match presentation.
"I would like to congratulate Novak. His record here is incredible. Very few people have managed to do what he has done here. He is a very well-deserved champion," he said.
"To his team... I know you can't do this on your own and he has great people around him.
"I'd like to thank my team - they've done a great job with me."
Djokovic said: "I have to thank Andy for his kind words.
"We have played so many thrilling matches over the last few years. Bad luck tonight and I wish you luck for the rest of the season.
"What a joy. It's an incredible feeling winning this trophy again. It's definitely my favourite grand slam, my most successful grand slam. I love this court."