West Indies captain Kraigg Brathwaite said lack of partnerships cost them the match.
Kieran Powell (83) then struck eight fours and four sixes in his 93-ball knock in Windies' second dig before becoming one of Kuldeep's victims, the bowler's figures of 5-57 beating the 4-40 he claimed against Sri Lanka in Pallekele in August 2017.
Ravindra Jadeja got three wickets in the second innings.
Resuming on 94-6, West Indies showed some fight as Roston Chase (53) and Keemo Paul (47) continued their seventh-wicket partnership from Friday evening and added 73 runs overall with some attacking batting. Sherman Lewis and Shanon Gabriel looked clueless and gifted their wickets away to the offspinner.
Jadeja had to wait till his 38th Test to reach three figures, having made his debut back in December 2012. Meanwhile, Team India humiliated Windies and registered their most significant victory in the longest format by winning the game by an innings and 272 runs.
Umesh Yadav ended the resistance when Paul fended off a bouncer in the 39th for a simple catch to mid-wicket. Virat Kohli and Ravindra Jadeja were the other centurions.
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Chase then chipped Kuldeep straight to Ashwin at extra cover and the wrist-spinner's fifth wicket came when Powell edged to Shaw at silly point.
Kuldeep ripped through the tourists' middle order, trapping Shai Hope lbw before dismissing Shimron Hetymer and Sunil Ambris in the same over.
'He had a real maturity for a young lad but he was also incredibly warm, good-humoured and quite cheeky, ' she said. "Well, we asked Kuldeep to give it a shot for you guys". They trail India by 555 runs and the hosts will fancy themselves to bowl them out twice by day three.
"We did talk about being positive in our team meetings".
After Prithvi Shaw's pehnomenal ton on debut on day one, skipper Kohli (139) and Jadeja (100 not out) made hundreds as India put up a mammoth 649 for nine in their first innings before declaring at tea. Can't imagine my debut like this. "I was looking to play my natural game, the way I play in First-Class cricket, and play the ball on the merit".
If day one was an indication between the gulf between two teams in different halves of worldwide arena, Friday widened the gap in the standard of cricket between India and the West Indies, with the hosts toying with the Caribbeans in all departments.