India were put into bat at Queen's Park Oval and got off to a perfect start with the first wicket falling on 123 when Shikhar Dhawan was caught off the bowling of Kemar Roach for 69.
That brought Kohli to the crease, and, despite wickets falling at regular intervals at the other end, the 24-year-old created a solid foundation and went on to score 102 from 83 balls which included 13 fours and two sixes.
He was eventually dismissed in the final over, caught by Darren Sammy off Dwayne Bravo, but the damage had been done as India finished their 50 overs with a total of 311 for seven.
Kohli accelerated the pace during his innings, moving from 35 off 45 balls to 102 off 83 to set India up with a good chance of securing a win.
Rohit Sharma (46) and useful knocks from Murali Vijay (27 from 18) and R Ashwin (25 from 18) at the end of the innings boosted the side's total, as no West Indian bowlers stood out.
Tino Best (two for 51) had the best figures. The bowling duties were shared by seven men, with only Sammy and Sunil Narine unable to take a wicket.
India could earn a bonus point if they restrict West Indies to 248.
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- Darren Sammy