The Serb triumphed 6-3 5-7 6-4 against the Scot in their first meeting since the ATP World Tour Finals final in November in London, when they played for the no1 ranking.
In what was the 36th meeting and 19th final between the world numbers one and two, defending Djokovic took the first set 6-3.
Murray, who won this title in 2008 and 2009, battled back in the second, however, after saving three match points in the 10th game of the set before winning it 7-5.
But it was Djokovic who had the final say as he won the third set 6-4 to claim his first title of the year.
Speaking after the win, Djokovic said: “It is definitely one of the best ways to start a year.
“When he turned it around, wow, I thought I hope this is not payback time for yesterday.
“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. We’re both going to need a little time to recover.
“To win here, against the biggest rival, is a dream start.”
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