Kohli struck his 20th one-day international century in Dharmasala, with his 127 helping the hosts to 330-6 off their 50 overs.
And Marlon Samuels' second century of the series was not enough to save the visitors, as they were dismissed for 271 in reply.
However, off-the-pitch matters are making the headlines as the remainder of the tour is unclear after the Board of Control for Cricket in India (BCCI) and West Indies Cricket Board (WICB) released contradicting statements.
The BCCI claimed the tour would end after Friday's match, but the WICB insisted no decision had been made.
Having been put into bat, India took full advantage as Ajinkya Rahane (68) and Shikhar Dhawan (35) put on an opening stand of 70.
All of India's top four contributed with Kohli (127) and Suresh Raina (71) - both of whom were dropped - carrying on the openers' good work by taking India towards the 300 mark.
Raina was eventually dismissed in the 45th over, but India were already in the driving seat before Kohli was run out in the final over.
West Indies' reply got off to a slow start and by the end of the second over Umesh Yadav (2-44) had made the breakthrough, having Dwayne Smith caught at mid-on for a duck.
Kieron Pollard for just six to leave the score at 27-2, although Darren Bravo (40) and Samuels helped settle things down.
The loss of quick wickets continued to hamper the West Indies and they saw Dinesh Ramdin (nine) and Dwayne Bravo (zero) removed within the space of three balls, leaving them five down for just 121 runs.
Samuels was joined at the crease by Darren Sammy (16), and the former took the game to India with excellent footwork, especially against Ravindra Jadeja (2-80).
Samuels and Andre Russell (46) tried in vain to get their side back into the match with a 57-run partnership for the seventh wicket, but India had too much for them.
Mohammed Shami (2-72) wrapped up the victory by removing Samuels and Jerome Taylor (11), but it remains to be seen whether the tour continues.