The dramatic match, which showcased the best of men's tennis for 2 hours, 54 minutes, required Djokovic to need four match points - three in the second set and one in the third - to prevail.
"Definitely one of the best ways of starting a year," Djokovic said on court. "After saving five match points in the semifinal, and I had three match points in the second set, I said, 'Wow' when he turned it around.
"All the way to the last shot you never know with Andy."
Murray's loss ended his 28-match winning streak that dated to Sept. 18.
Djokovic had three match points in the 10th game of the second set, but couldn't prevent Murray from making it 5-5 and eventually winning the second set.
Murray finally capitalized on his fourth break point - second in that 10th game - with an inside out forehand winner.
Despite going up 0-30, Murray wasn't able to come up with the same magic when Djokovic served for the match a second time at 5-4 in the third set. Murray also failed to take advantage of a break point in the sixth game of the third set.
"Physically, it was a good test to start the year," Murray said. "My body feels all right just now, so that's positive.
"Still think there are things I can do better. I wasn't that clinical on break points this week, which maybe that comes with playing a few more matches."
Djokovic's frustration got the better of him on two particular moments in the match, which caused umpire Carlos Bernardes to hand the Serb two warnings, including the loss of a point on the second warning.
The second warning resulted when Djokovic smashed his racket in frustration at 40-30 to end the 11th game of the second set, which Murray was serving for, prematurely.
The first warning came in the sixth game of the first set.
Annoyed at losing a point, Djokovic angrily smacked a ball to the ground that accidentally flew into the stands and hit a woman.
The top-ranked Murray has lost all 20 matches he's played against Djokovic when he's lost the first set.
Overall, Djokovic held a 25-11 career record over Murray.
Murray won their last encounter 6-3, 6-4 in the ATP Finals in November. That victory catapulted Murray ahead of Djokovic to the year-end No. 1 ranking for the first time.