The scores 6-2, 7-5 gave the fourth-seeded Murray his 11th title in 17 career finals.
The Scotsman also became the first three-time winner on the men's tour in 2009 after capturing the Qatar Open at Doha in January and the ABN AMRO World Tennis Tournament at Rotterdam in February.
"He started to come to the net a bit more and I lost my timing a bit but I was able to get it back," Murray replied to a question about his opponent and the windy weather conditions.
He beat Djokovic for the third consecutive time after dropping the first four meetings with his Serbian opponent. His victory was worth a $605,500 paycheck.
Djokovic was trying for his 13th career title and second this season.
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