India, set 212 to win, suffered an early set back when Shikhar Dhawan was dismissed for just five but Sharma (72 from 81 balls) and Kohli (86 from 84 balls) quickly got the hosts back on track.
And by the time the pair were dismissed, it was too late for West Indies to launch a fightback as Yuvraj Singh (16 no) and MS Dhoni (13 no) quickly added the remaining runs to seal a convincing win with the loss of only four wickets.
West Indies opener Chris Gayle was stretchered off with a leg injury to leave his participation in the three-match series in doubt.
“I was timing it very well and once I gained the confidence, I just carried on,” said man of the match Kohli.
“I tried to keep the bat close to the body and once you get into good positions even if the ball keeps low you can handle it.”
India captain Dhoni added: “I think it's a fantastic performance and it could have been ever better if one of our batsmen had got a hundred.”
Darren Bravo made 59 for West Indies in their innings as Ravindra Jadeja and Suresh Raina took three wickets each.
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- Yuvraj Singh
- Shikhar Dhawan