Djokovic's victory was his third at Miami and avenged his 2009 loss to Murray here at Crandon Park.
"I thought I played a great match from the start to the end," Djokovic, who did not drop a set throughout the tournament, said during an on-court interview.
"But with such a quality player you really never know, that's why he's right at the top. He always comes back even if you feel that you have control of the match so I am really happy to close it out in straight sets."
The Serb got a grip on the match, breaking in a long and compelling fourth game when Murray twice made unforced errors on his backhand on game point.
The Scot responded positively and had break point on the next service game from Djokovic but his opponent turned on the power to hold.
Murray's backhand let him down again in the next game and two shots into the net allowed the Serb to break and serve out to take the set comfortably.
The second set was tighter but Murray had to work much harder to hold his serves and failed to get a break point against the confident 24-year-old.
Djokovic ran out 7-4 winner in the tie-break to follow up his Australian Open title with his second win of the year.