He faces Juan Martin del Potro next, who made short work of lucky loser Jeremy Chardy to win 6-1 6-3 and book a place in the semi-finals of the tournament in Mason, Ohio.
Second seed Djokovic married brilliant defensive play with seven aces and Cilic, who had lost all six of their previous meetings on the tour, had no answers.
The 12th seed saw a 40-0 lead on his first service game turn into a break of serve, and Djokovic served out with confidence to seal the set.
The second set was more clinical still. Djokovic had won the Rogers Cup in Toronto last weekend, and looked refreshed after a virtual day off yesterday, when opponent Nikolay Davydenko withdrew from their match after just six games - all of which he lost - with an injury.
The Serb broke twice more, and despite allowing Cilic a look at a couple of break points when serving for the match, he snuffed out the chance and closed out the match.
A rematch of the Olympic bronze medal match awaits the world number two next - Djokovic lost out to Del Potro in London - and will be keen for revenge.
"It was my best match so far here in this tournament and came in the right moment, really," Djokovic, who had an easy passage through to the last eight after Russian Nikolay Davydenko retired injured during their match, said.
"I had the biggest challenge today with Cilic who has been playing well the last couple of months and I played a really good match."
The five-times Grand Slam winner may have added incentive on Saturday given Serbia's Davis Cup semi-final loss to Argentina last year in which Djokovic retired against Del Potro.
"All these losses made me stronger and, yes, they are difficult, especially when you're playing for a country and when you're in Olympic Games and we're fighting for bronze medal," said Djokovic.
"He won that match. It happens. It's a sport. You lose, you win, but the most important thing is to try to move on and become even better and even stronger from those experiences and try to win."
The Argentine had few troubles against Chardy. The Frenchman had only made the main draw as a lucky loser, but took full advantage to down Andy Murray in the previous round. But the forehand that had stood him in such good stead all week was misfiring, and the unforced errors piled up.
Del Potro for his part was patient and pragmatic, waiting for the match to fall into his lap.
He claimed four breaks of serve in the match - though it could have been over still quicker had the Argentine not missed out on a further 13 break points.
Nonetheless, after a wobble in the previous round against Viktor Troicki, and some concerns over an injury to his left wrist, the Olympic bronze medallist was in good touch and looked full of confidence.
- Juan Martin del Potro