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Johnson Charles top-scored with 45, but it was of little value as India dismissed the hosts for 171 with five overs remaining.
Buvneshwar Kumar and Umesh Yadav took three wickets each.
The match was interrupted by rain with the West Indies on 56 for two after 10 overs and a revised target of 274 off 39 overs were set.
Earlier, Virat Kohli powered his way to a 14th one-day international century to lift India to a challenging total of 311 for seven batting first.
Earlier, with his team in desperate need of a lift after defeats in their opening two matches earlier in the week in Jamaica, Kohli played the quintessential captain's innings, his 102 off 83 deliveries with 13 fours and two sixes building on an excellent platform provided by the openers and leaving the hosts with a daunting task if they are to maintain a 100 percent winning record in the competition so far.
He came to the crease in the 24th over after Shikhar Dhawan (69) and Rohit Sharma (46) had given the World Cup holders the ideal start on a sweltering morning, putting on 123 for the first wicket.
Left-handed Dhawan was the more aggressive, hoisting spinner Sunil Narine for consecutive sixes and setting the trend for a more assertive effort from the Indian batting line-up.
Sharma seemed intent on playing the supporting role, especially with Kohli keen to impose himself and dismiss speculation that his team was lacking in commitment so soon after their Champions Trophy success in England.
He struck the ball cleanly and powerfully from the start of his innings, and even though wickets were falling regularly at the other end, the attacking right-hander was able to gradually raise the tempo to the point that he was in full cry and dominating a seventh-wicket partnership of 90 with Ravi Ashwin (25 not out) off just 52 deliveries.
Tino Best's persistent pace and never-say-die effort brought him two wickets, but West Indies captain Dwayne Bravo made some puzzling tactical choices in the use of his bowling resources.
A clearly off-colour Narine was restricted to five overs but former captain Darren Sammy, who opened the bowling and conceded just 28 runs off eight overs, was not summoned to stem the tide over the final few overs.
Bravo himself proved the most expensive, being plastered for 57 runs off seven overs, although he did have the minor consolation of claiming Kohli's wicket off the final ball of the innings.
