The 20-year-old Cilic struggled at times against the 202nd-ranked Devvarman but saved nine of 10 break points to hold off the home favorite, who was playing his first ATP final.
Cilic was serving for the match at 5-3 in the second set when Devvarman finally converted a break point, but the Croatian used his strong serve to dominate the tiebreaker. Cilic finished with nine aces, to Devvarman's one.
Devvarman had a number of chances to take control of the first set, going up 40-0 on Cilic's serve in the fifth game. The Croat recovered, however, and then saved two more break points in his next service game and got the decisive breakthrough in the 10th game, when Devvarman double faulted on set point.
Cilic took a 3-0 lead in the second before the Indian rallied to force the tiebreaker.
Cilic, a semifinalist here in 2008, won his first tour title at New Haven, Connecticut, last year.
The 23-year-old Devvarman, who won the NCAA collegiate titles in 2007 and '08 as a student of the University of Virginia, was the first Indian to reach the final of the event, which began as the Indian Open in New Delhi in 1996 before moving to Chennai the following year.
"It's great to start the year with a title win, I've been in training hard for the new season,'' Cilic said. "It wasn't my best show, but I played the crucial points well.''
As for Devvarman's rally in the second set, Cilic said: "A few loose points during my loss of concentration took that set to the tiebreaker.''
The Croatian now plans to travel to Melbourne, play a couple of exhibition matches and train for the Australian Open.
Devvarman, who paid the price for his missed opportunities, said: "Losing is not fun, not converting the break points wasn't my best move.
"Marin plays high-percentage tennis and produced a great game today. He came up with good shots even when under pressure.''
Only three Indians have won ATP Tour titles - Vijay Amritraj (16 titles), Ramesh Krishnan (8) and Leander Paes (1).
Paes was the last Indian player to win an ATP Tour title, at Newport in 1998.
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