The West Indies batting lineup failed to withstand the Indian attack's fifth day onslaught as they collapsed to a total of 108 all out.
After a brief batting blitz in the morning session India declared on 217 for 7 leaving the West Indies a target of 345 to win, and themselves 87 overs to bowl the hosts out.
Ajinkya Rahane finished unbeaten on 71 and Miguel Cummins was the pick of the West Indies bowlers as he benefited from the attacking approach of India to take 6 for 48.
The West Indies response was more than a little disappointing, they showed none of the grit and determination that had helped them save the second Test, as they fell well short of saving the game, suffering a 237 run defeat.
Darren Bravo was the only batsman to acquit himself reasonably well as he scored 59 off 178 balls, his dismissal signaling the end of what little resistance the hosts had shown.
Mohammed Shami got the early breakthrough removing Leon Johnson for nought, caught at short leg.
Shami finished with figures of 3 for 15 and also got the wicket of Bravo and Shane Dowrich (5).
Each of the Indian bowlers contributed wickets to the cause, Ishant Sharma removed Marlon Samuels (12) and Roston Chase (10) bowling them both.
Ravindra Jadeja had Jermaine Blackwood stumped for one and took the winning wicket as Shannon Gabriel holed out for 11.
First innings hero Buveshnar Kumar picked up the wicket of Kraigg Brathwaite and Ravi Ashwin got Alzarri Joseph for a duck.
India take a 2-0 lead in the series and look set to reclaim the top spot on the ICC Test rankings.