Djokovic, who will return to world No. 1 next week, had his personal best winning sequence of 30 consecutive sets ended as Cilic played almost flawlessly aggressive tennis to draw first blood in a magnificent duel.
Yet it only prompted Djokovic to increase his focus and produce some supreme play to turn the tide and prevail 4-6 6-2 6-3.
So intense was the Serb that even when he was fighting back in the second set, leading 5-2, he ended up screaming at his team at the top of his voice, demanding to know why he had not received the vitamin tablets he had been asking for.
After being broken to go 2-1 down in the final set, Djokovic smashed his racket, accepted the code violation and steamed with anger in his seat before immediately breaking back.
When in more peril at break point down at 3-3, Djokovic delivered an amazing game-saving backhand at full stretch, which perhaps helped break Cilic's spirit as he squandered the next game before succumbing in two hours 11 minutes.
Earlier, Russian Karen Khachanov pulled off one of the big surprises of the tournament when he outplayed top young gun Alexander Zverev 6-1 6-2 to reach the other semi against Dominic Thiem, who beat defending champion Jack Sock 4-6 6-4 6-4.
Khachanov, at 22 another of the sport's brightest prospects, took ruthless advantage of the 21-year-old German's physical struggles as Zverev, battling with shoulder trouble, needed a medical time out in the first set at 4-1 down.
The Muscovite deserved all the credit for the quality of his power game, however, as he broke the world number five's serve six times in 70 minutes to set up a date with Austrian Thiem, who beat champion Jack Sock 4-6 6-4 6-4.
Sock had made an unexpected return to form after a wretched year since his surprise Paris triumph but his renaissance was ended when Thiem fought from a set down to take control in a tough two-and-a-quarter hour duel.
The victory gave French Open finalist Thiem a further boost in his bid to earn one of the final two of eight places on offer for the ATP Finals in London this month.
"Jack was playing a great game and had a very good start and it was a great fight again, but it's really something special for me to reach this stage," world number eight Thiem said. (Reporting by Ian Chadband; editing by Martyn Herman and Ed Osmond)
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