The Serbian world No. 1 had to bounce back from losing the first set on top of losing last year's US Open final to Murray, but in the end he cruised through the third and fourth sets to prevail over the Brit world No. 3, 6-7 (2), 7-6 (3), 6-3, 6-2 in three hours and 40 minutes.
By winning, Djokovic has now won six Grand Slam titles with four of those coming at the Australian Open. By claiming three in-a-row in Melbourne he has become the first man to do so in the Open era, and the first since Australia's Roy Emerson won five straight between 1963 and 1967.
Ken Rosewall, Guillermo Vilas, Johan Kriek, Mats Wilander, Stefan Edberg, Ivan Lendl, Jim Courier, Andre Agassi and Roger Federer have all won consecutive Australian Open men's titles, but never were able to do what Djokovic now has in winning three.
Murray was playing in his third Australian Open final after losing in straight-sets to Federer in 2010 and Djokovic in 2011, and started well by winning a set for the first time in the three finals but then things started to wrong.
Djokovic cruised through the second set tie-break and then dominated the third and fourth sets as Murray had trouble with a sore foot, and was showing signs of wear and tear after his almost five-hour, five-set semi-final marathon win over Federer.
Murray came into the Australian Open with renewed confidence having won Olympic gold last year at Wimbledon and then winning his first Grand Slam title at the US Open, but the longer the final on Sunday went the more signs of the old temperamental Scotsman came out again.
Djokovic had the best, and first, chances to break serve in the sixth game of the opening set but eventually Murray held on after surviving four break points.
That proved the only meaningful chances of a service break in the first set as well as it went into a tie-break where Djokovic immediately double-faulted. Murray then held his first two serves of the tie-break to race to a 3-0 lead and the Scot wasn’t about to let the advantage slip taking it out 7-2.
While it was Djokovic that could not capitalise on five break point chances in the first set, it was Murray that didn’t grab his opportunities in the second as it went to a second straight tie-break.
With help from a wayward feather that distracted Murray enough for him to double-fault, Djokovic raced to a 6-3 advantage in the tie-break and held serve the next point to level the final up at a set apiece.
Murray then took an injury timeout to receive some treatment on his foot at the end of the second set and it took until the eighth game of the third set, but eventually the first break of serve of the match came and it was to Djokovic.
From there he cruised to take out the set 6-3 and then raced out to a 4-1 advantage in the fourth set to be on the brink. The Serb had no trouble closing the match out serving for the match at 5-2 and having no trouble doing so to start off his 2013 the same way he has his 2008, 2011 and 2012.
Djokovic was rightfully ecstatic with his sixth Grand Slam victory.
"I have to congratulate Andy and his team for a great two weeks. We have played so many thrilling matches the last two years and hopefully we can have many more to come," Djokovic said.
"What a joy this is. It's an incredible feeling winning this trophy once more and it's definitely my favourite Grand Slam, and my most successful Grand Slam. I love this court."
Murray was gracious in defeat acknowledging just how tough Djokovic is to beat in Melbourne.
"I'd obviously like to congratulate Novak," Murray said.
"His record here is obviously incredible and there are very few people who have managed to do what he has done here, so he's a very well-deserved champion."