Murray overcame a game Dimitrov, who was appearing in his first ATP final, for a 7-6 (7-0), 6-4 victory.
Murray dropped his first game on serve and saved a set point to force the tiebreaker, which he swept by finishing off the set with an ace. He fell behind again in the second set after Dimitrov broke in a 10-point game before taking the final three games of the match. That run included a pair of break points.
It marked the 25th ATP title in Murray's career, which is fifth most among active players.
Murray won $78,800 to go along with the championship. Dimitrov collected $41,540.
Swim Week Miami Beach 2014 [PHOTOS]