Federer clinched his fifth Dubai crown without dropping a set all week. He broke Murray at 5-5 in the first set as the Briton's serving dipped.
The Swiss, 30, then broke again to go 3-1 ahead in the second set but Murray produced two brilliant lobs to square the set at 3-3.
Federer remained unfazed by his opponent's fightback and attacked Murray's second serve to force the Briton to net a backhand for a decisive 5-4 lead.
Serving for the match, Federer hit a series of stinging forehands into left court to earn match point and he sealed victory with a blistering winner past a subdued Murray.