Djokovic looked in firm control at a set and a break up, enjoying a 5-3 lead in the second and serving for the match.
But Murray dug deep and produced some stunning tennis to save three match points and break back - extending his streak of consecutive matches with at least one break of serve to 112.
The momentum switched entirely. and Murray reeled off five straight games to take the second set and go 1-0 up in the third.
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The Serb seemed to be falling apart at one stage, ranting on court and then losing a game after being penalised a point for smashing his racket for a second time.
But as so often, Djokovic dug deep and found extra reserves of energy - just when he looked at his lowest, he broke again. Despite taking a 0-30 advantage as the Serbian served for the match a second time, Murray could not turn the tables again.

Djokovic in furious rant after Murray breaks back at crucial moment

Djokovic won an epic three-hour encounter, and we will be lucky to see the same again in the Australian Open final three weekends from now.
He said: "It's definitely one of the best ways to start the year.
"All the way to the last shot you never know with Andy. It's no strange occurrence for both of us to play three sets for three hours. It's a very physical battle and we're both going to need some time to recover from that and get ready for Melbourne."

Djokovic: Win over Murray one of best ways to start the year

Despite the result Murray actually extends his lead at the top of the rankings, as he did not play a tournament this week last year while Djokovic won in Qatar.

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