Despite a mediocre first serve percentage, the unseeded Kyrgios did not face a break point in the opening set, while former U.S. Open champion Cilic dropped his serve twice.
World number 41 Kyrgios, playing his second ATP final after a runner-up finish in Estoril last year, sent down 17 aces as he completed victory over Cilic.
Opinion: No multiple major winners again, but Barty’s 2021 season should be given more respect
It concluded a dramatic breakthrough week for Kyrgios, who had previously garnered almost as many headlines for his on-court misbehaviour as his obvious rare ability.
The man from Canberra also beat two top-10 ranked players in Richard Gasquet and Tomas Berdych plus the 12th-ranked Cilic, and did not lose a set in the tournament, his serve being unbroken in 47 games.
Kyrgios, whose ranking of 41 will shoot up, was playing in his second ATP final after finishing runner-up in Estoril last year but his maiden victory seems sure to be the first of many.
He is the first player under the age of 21 to down top 10 players in consecutive matches since Juan Martin del Potro beat Rafa Nadal and Roger Federer to lift the 2009 U.S. Open crown.
"I played my first final last year and was looking for my first title," a delighted Kyrgios told the ATP website.
"But I didn't really expect to win this title this week after having a couple of weeks off. But from the first round I started playing really well and just gained confidence as I kept winning matches."
Kyrgios had to withdraw from a tournament in Rotterdam the previous week with an elbow injury but showed no signs of discomfort as he put Cilic under pressure from the start.
He converted his eighth break point for a 3-1 lead in the opening set before capturing a second break in the seventh game and then serving out to love to take the set.
Cilic had a chance to force a decider with a set point in the 10th game but Kyrgios held firm and served out the match with an ace in the tiebreak after 85 minutes.
Kyrgios's elation in his second tournament of the season was a far cry from some of last year's negative headlines.
In August, the Australian received a suspended 28-day ban and a $25,000 fine for a vulgar comment he made towards Stanislas Wawrinka at the Rogers Cup in Montreal.
Two months later, Kyrgios was fined for a verbal outburst during his first-round match at the Shanghai Masters.
He began the year in eyebrow-raising fashion by answering his phone on court before a mixed doubles game at the Australian Open.
Raducanu US Open win a 'massive opportunity’ for tennis says Murray
Team Europe lift the Laver Cup trophy in 2019 after securing hat-trick of titles