Kohli notched up his 14th ODI century as the Indians posted a challenging 311 for seven before bowling out the hosts for 171 in 34 overs to grab a bonus point via the Duckworth/Lewis method in the rain-truncated match.
The target was revised to 274 in 39 overs after a two-hour rain delay before which the hosts were 56 for two in 10 overs. This was India's first win in the series after losing both their first-leg matches.
West Indies are in with a stronger chance having won two of their three matches for nine points. They they will wind up their league engagements tomorrow against Sri Lanka.
India will face Sri Lanka on Tuesday in the last league match. Both the teams have five points each as of now.
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After a couple of ordinary shows, the famed Indian batting line-up got its act together with Kohli leading the way.
Batting with a lot of grit and gumption, Kohli (102) anchored India after the team lost five established batsmen at a score of 210 in 40 overs.