Kohli (143 batting) led from the front to lay a solid platform for his team with the other major contribution coming from opener Shikhar Dhawan (84).
The Indian captain, who also crossed the 3000-run mark in his 42nd Test, had the support of Ravichandran Ashwin (22 batting) at close of play as the two shared an unbeaten 66-run stand.
The away side had a rather quiet first session where it managed 72 for one in 27 overs before Kohli arrived at the crease and stepped up the tempo. By stumps, India had a decent run rate of 3.35 runs per over.
The pitch was flat and the West Indies bowling lacked depth to trouble the visitors who found it tough early on after Kohli opted to bat.
Starting at 65 after tea, Kohli put on 57 runs with Ajinkya Rahane (22) as the duo looked to build after losing both Dhawan and Cheteshwar Pujara (16) in the second session of play. Rahane was nearly dismissed cheaply, for 5 runs, as Shannon Gabriel (1-43) induced an edge that fell short of slips. But thereafter the vice-captain tightened up his game and didn t give another chance until his eventual dismissal.
In the meantime, the duo kept the run-rate flowing, bringing up the 200-mark in the 61st over. Then, five overs later, they brought up their 50-partnership, coming off only 65 balls. Kohli was looking particularly good in this period, as cover drives and on-drives started booming off his blade.
Perhaps Carlos Brathwaite (0-46) was the only bowled who troubled him a bit, but even was not able to create a straightforward wicket-taking opportunity.
Just as they were looking good, Rahane was dismissed, a loose stroke off Devendra Bishoo (3-108) lobbing up and he was caught at midwicket. It was yet another loose dismissal for India, with only Murali Vijay (7) getting out to a good delivery earlier in the morning.
Thereafter, with 22 overs remaining in the day's play, it was surprising to see Ashwin come out to bat ahead of Wriddhiman Saha.
But he did an immaculate job, including some silken drives down the ground, and the two batsmen stayed unbeaten until the end of play, bringing up the 300-mark in the 88th over. Kohli and Ashwin's stand partnership rescued India from what looked like a disappointing first outing for the five top-order batsmen theory.