Kohli struck 10 boundaries from 104 balls, and Sharma hit two fours and one six from 72 deliveries in a 110-run stand for the second wicket, propping up the Indians after they were sent in to bat on a hard, bouncy Sabina Park pitch, and stumbled to 79 for three in the 17th over.
When Kohli was run out in the 36th over, failing to beat Ramnaresh Sarwan's throw to wicketkeeper Carlton Baugh Jr going for a second run, the visitors batting collapsed under mean, purposeful West Indies bowling.
The world champions lost their last seven wickets for 62 in the space of 70 deliveries, as Andre Russell, playing an international match for West Indies on home soil for the first time, captured four for 35 from 8.3 overs.
Yusuf Pathan threatened to turn the tide for India, but Russell had him caught behind for 30 in the 46th over at the height of the carnage.
Kieron Pollard took two for 39 from eight overs, and Kemar Roach two for 52 from his allotment of 10 overs to support Russell in the demolition of the Indian batting.
West Indies made one change to their line-up for the match, with opener Adrian Barath making his return, following a five-month injury lay-off, nursing a damaged hamstring.
The Indians made two changes - Subramanian Badrinath and Praveen Kumar are not playing, so Shikhar Dhawan returns after missing the previous match, and Vinay Kumar plays his first match on the tour.
The visitors were looking to sign-off the ODI series with a resounding victory, after they stumbled in the fourth ODI two days ago, losing by 103 runs at the Vivian Richards Cricket Ground in Antigua.
The world champions still hold an unbeatable 3-1 lead in the series, after victories in the first three matches.
But they will want to finish strongly, bringing West Indies back down to earth, particularly with a three-Test series immediately following.
