Batting with a lot of grit and gumption, Kohli anchored India to a challenging 311 for seven after his side was in a spot of bother, having lost five established batsmen at a score of 210 in 40 overs.
Openers Shikhar Dhawan (69) and Rohit Sharma (46) had laid a strong foundation with their 123-run stand and Kohli (102) ensured that their hard work does not go waste as he made up for the failure of the middle-order with his gritty 14th One-Day century.
West Indies had a daunting task of scoring a further 218 runs from 29 overs after resuming at 56 for two in 10 overs.
India, desperately requiring a win to remain in the hunt for a berth in the final, bowled out the hosts for 171 in 34 to walk away with a bonus point.
India's victory meant that the tournament is open with all three teams having a chance to qualify for the final. West Indies next play Sri Lanka on Sunday and then India face Sri Lanka on Tuesday in the last league match.
Sharma had Marlon Samules (6) caught and removed set opener Johnson Charles (45) while Kumar added wicket of dangerous Kieron Pollard, who could not even open his account.
Umesh Yadav (3/32) joined the party by scalping Denesh Ramdin (9) and rival skipper Dwayne Bravo (14) to leave West Indies reeling at 108 for six.
Earlier, 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 good position with regular strikes.
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.
Kohli responded to the challenge in the best possible manner as India scored 101 runs in the last 10 overs and his contribution was 67 runs. 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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