West Indies were 56 for two after 10 overs when rain halted play with Johnson Charles (33) and Marlon Samuels (5) at the crease.
Young paceman Bhuvaneshwar Kumar dismissed dangerous Chris Gayle (10) and Darren Barvo (1) inside five overs. Aided by bounce off the pitch, Kumar had Gayle caught behind and Darren caught in the slip region.
Earlier, Kohli hit a fighting century to power India, desperately looking for a win after consecutive defeats in first two matches, to a decent total.
Kohli got out in the last ball of the innings as he nullified the success of West Indies fast bowlers, who had put the hosts in an advantageous position with regular strikes.
Kohli faced 83 balls in his innings, his 14th One-day century, and punished the Caribbean bowlers with 13 fours and two sixes.
After 40 overs, India had 210 runs on the board and only Kohli to bat with tail-enders as pace duo of Kemar Roach and Tino Best had polished off the Indian middle-order.
R Ashwin supported Kohli well with his 18-ball 25 as they shared a 90-run stand for the seventh wicket in 8.2 overs.
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