The 31-year-old Serb took his chances with a couple of crisp forehands in the 12th game to break the Cilic serve and claim the first set after an hour long battle.
A rampant Djokovic conceded just one point on his first serve during the second set and looked favourite to close out the contest and claim a first title for 12 months.
Cilic netted a backhand to give the Serb a match point in the 10th game, but he responded with a booming serve out wide.
Djokovic, who had won 14 of his 15 matches against Cilic, then led 4-1 in the ensuing tiebreak but seemed to tighten up, and a double-fault at 4-4 gave Cilic the momentum to level.
Cilic looked the stronger player in the decider and a superb running forehand pass gave him a break point at 3-4 before Djokovic hit a backhand into the net to drop serve.
All that was left was for Cilic to hold his serve, and he did so with a love game to claim his first title of the year and head for Wimbledon in high spirits.
"I was just trying to stay mentally in it. And definitely, it was an extremely tough match," Cilic said.
"No breaks for me until that last (return) game. I definitely feel relieved that I won it and what a great week."
Djokovic will be concerned that he allowed a match in which he appeared to be in control slip through his fingers, although he has shown signs of a return to form after his struggles of earlier in the year following a minor elbow operation.
"Obviously disappointed not to be able to win it, because this was, you know, a big occasion for me playing finals against Cilic, who is obviously one of the best players in the world," three-times Wimbledon champion Djokovic said.
"I thought I have built up the momentum quite well throughout the week. Played great. It wasn't to be, unfortunately. Double fault at 4-3 up (in the tiebreak). Yeah, I got a little bit tight there. Obviously he used it."
"But I can definitely take a lot of positives this week."
(Writing by Hardik Vyas in Bengaluru and Martyn Herman; Editing by Ken Ferris and Hugh Lawson)
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