Kyrgios closed out the match with his 17th ace to cap a dream week for the 20-year-old Australian, who didn't lose a set and was unbroken in 47 games. Ranked 41st, he beat two top-10 players in No. 10 Richard Gasquet and No. 8 Tomas Berdych.
It was only Kyrgios' second tournament of the year. He lost to Berdych in the third round of the Australian Open in January and was forced to withdraw from Rotterdam last week with an elbow injury.
"I didn't really expect to win this title this week after having a couple of weeks off," said Kyrgios, who lost his only previous final on outdoor clay last year in Estoril, Portugal. "But from the first round I started playing really well and just gained confidence as I kept winning matches.
"I think I served really, really well again. I was serving really well all week. I didn't get broken once. That was the main thing that was good. And I was able to put pressure on my opponents' serves a lot when I was going through my service games really quickly."
The popular Kyrgios ended his victory speech with a few words of French, declaring to his fans, "I really like cheese."
Kyrgios had Cilic under pressure from the start and converted his eighth break point to go 3-1 up in the first set and never looked back, securing a second break in the seventh game before serving out the set to love.
Cilic fought back in the second set and almost leveled the match in the 10th game, but Kyrgios saved the only break point he faced in the contest with a 201 kph (125 mph) ace.
"I felt I was getting much closer in that second set," Cilic said. "I felt also that he was becoming a bit more frustrated, which was good for me. I had a chance at the end of the second set to get the break, but he managed to play well. ... I didn't adjust well enough on the balls that were coming back."