Kohli scored 200 as India hit 566 for eight declared, sharing a 168-run fifth stand wicket with Ravichandran Ashwin (113), who was dropped on 43 by wicketkeeper Shane Dowrich and made the West Indies pay by compiling a century.
West Indies were 31 for one in their first innings at the close of play with Kraigg Brathwaite (11) and nightwatchman Devendra Bishoo (0) at the crease.
Rajendra Chandrika went for 16 in the penultimate over of the day when he got a thick edge to the keeper off paceman Mohammed Shami.
The day belonged to Kohli, who completed his double tonne just before lunch by pulling a single to deep mid-wicket.
He went down on his knees and kissed the turf as retired West Indies great Viv Richards, after whom the venue in North Sound is named, joined in the applause from the stands.
Kohli, who struck 24 fours in 283 balls, was out shortly after lunch when he got a thick inside edge on to his stumps off fast bowler Shannon Gabriel (2-65).
Leg-spinner Bishoo (3-163) looked dangerous at times but for the most part the home attack posed few problems for the batsmen on a flat track.
Ashwin, who registered his third test century, said a more disciplined approach was the key to his success.
“I’ve been looking forward to this opportunity,” he said in an on-field interview after being promoted to number six in the order. “I really enjoy my batting and there have been times in the past when I’ve been a little too flashy.
“I know if I have to get into the top seven or six I really need to tighten my game so I’ve really worked on it. I’ve never left so many balls (outside off stump) in my life.”
India’s total left West Indies looking to occupy the crease for three more days to squeeze a draw in the first of four tests between the teams.
“It’s not going to be easy. We’ll have to prise every wicket out,” said Ashwin.