Jasprit Bumrah dismantled the hosts with a five-wicket haul after Ajinkya Rahane found his first century in two years as India won the first Test by 318-runs.
Resuming the day at 185 for three, Rahane scored an important 102-run knock. The patient innings came off 242 balls with just five shots to the fence.
Young batsman Hanuma Vihari (93) missed out on his maiden Test ton by just seven runs as India declared on 343/7, giving the Windies a target of 419.
It was a Bumrah show in the second innings, as he ended with the figures of 8-4-7-5, becoming the first Asian to take 5-wicket hauls in South Africa, England, Australia and West Indies.
Ishant Sharma (3/31) and Mohammed Shami (2/13) too contributed in India's resounding victory which gave them a 1-0 lead.
Ajinkya Rahane (81 and 102) was named the Man of the Match.
Virat Kohli has now the joint-most number of victories as India captain with MS Dhoni (27). He also went past Saurav Ganguly (11) for most away wins as India captain.
The win gave India 60 points in the World Test Championship, and the side sits at the top of the table.