The second-seeded Serbian broke Cilic's serve in the sixth game and again in the eighth to take the first set following a 90-minute rain delay.
The second set was a far more mixed affair, with each breaking the other's serve three times to force the tiebreak. That too was close but Cilic struggled to keep up, and his return at 6-4 went wide, handing Djokovic the win on Sunday.
The third-ranked Djokovic's path to the title was eased by Cilic's upset victory over top-seeded Rafael Nadal in Saturday's semifinal.
"Even though it was a straight-sets win it could easily have gone the other way. I think I was a little bit saved by the rain delay," said Djokovic, who has won all four meetings between the two. "I kind of got together my nerves to play well."
Cilic said the rain delay may have affected him.
"First time I went out on the court I started pretty good but when we came back the conditions were a little bit different. It was a little cooler and Novak started really good and I missed my shot to get back into the game," Cilic said.