Djokovic, ranked number three in the world, defied the blustery conditions to beat the world number two 3-6, 6-2, 6-3 in one hour and 46 minutes.
Federer, the 13-time Grand Slam champion, who is in search of his first title of 2009, comfortably won the first set as Djokovic found his feet, but could find no answers after that - finishing with 35 unforced errors.
"Novak played bad at the beginning, and I finished worse than him," said Federer, who lost seven straight games bridging the second and third sets.
That span included four breaks of Federer's serve, after he had had surrendered his serve just once in the tournament and contributed to a rare glimpse of temper from the normally restrained Swiss, who broke a racquet after yet another forehand miss in the third game of the final set.
"You try hard and then it's just not working," Federer said.
"Today it is different just because there's so much wind as well. Once you start feeling bad, it's kind of tough to regroup."
Djokovic said the windy weather and some early nerves both played a role in his shaky start.
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