The world number three beat Fish 6-2 5-7 6-3 to avoid the same fate that befell Roger Federer in the semi-final.
Djokovic followed up his own semi-final rout of Rafael Nadal by halting a magnificent week by Fish, who defeated three top-10 opponents, including the world number one. Fish did not succumb easily, rallying from a 4-2 deficit in the second set by breaking the Serb twice to force a decisive third set.
Djokovic, though, broke the unseeded American in the second game for a 2-0 lead en route to his second title of the year after his maiden grand slam at the Australian Open.
It was the second straight appearance in the final for Djokovic, who lost to Nadal a year ago.