Federer, 32, rarely troubled the Serb in the first set and the pivotal moment came at 2-2 in the second when the Swiss saved a break point with a delicious backhand pass.
The 17-times grand slam champion went on to hold serve and then broke in a rain-interrupted game - the players leaving the court for only a few minutes - with a backhand bullet from the baseline.
Federer clinched the set with an ace before Djokovic, 26, double-faulted in the first game of the decider to gift his opponent a crucial early break.
The five-times champion next meets Czech Tomas Berdych who subdued German Philipp Kohlschreiber 7-5 7-5 to record his 11th straight win and reach a second successive Dubai final.
(Editing by Tony Jimenez)
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