West Indies resumed on 94-6 after their top order collapsed in the final session on day two, facing a huge first-innings deficit following centuries by Kohli, Prithvi Shaw and Ravindra Jadeja.
Kuldeep returned figures of 5-57 with his left-arm wrist spin, his first five-for in just his fourth Test since making his debut against Australia past year.
On the eve of the second Test, Kohli, while heaping praises on the young gun, also urged the cricketing world to give him time to develop. Having endured a poor year that has seen Rahane score only two half-centuries in 14 tests, Rahane failed to impress against a listless West Indies side in Rajkot as well, getting just 41 on the board.
While 18-year-old Prithvi Shaw expectedly hogged the limelight with a smashing ton on debut, Kohli's innings was a master-class of how to set a different challenge for oneself as a batsman.
Nhlanhla Nene relieved of his duties, Tito Mboweni appointed new Finance Minister
"We wish Minister Mboweni well as he journeys through the mammoth task of steering our economy in the right direction". Ramaphosa said Mboweni, the former Governor of the Reserve Bank, brings in much-needed leadership.
Rahane has gone without a Test hundred for almost 14 months (last hundred came against Sri Lanka in August 2017).
Bishoo was the most successful bowler for West Indies with 4-217 and, in worrying signs for their own batsmen, got some balls to turn past the Indians.
Mohammed Shami took two wickets. However, the openers will be soon heading to the national side after the Test series against Windies is completed.
Left-handed opener Kieran Powell hit an attacking 83 while Chase chipped in with 20 but the Indian spinners weaved a web around the tourists, further extending their 24-year wait for a victory on Indian soil. Even though the big names are missing in the list, Cricket West Indies are viewing this ODI series as a platform for the young bloods to groove themselves ahead of ICC Cricket World Cup 2019 to be played in England.
Chase followed with 12 runs added, bowled off the inside edge, attempting to drive Ashwin and in the same over, debutant Sherman Lewis played back and was also bowled by one he mis-read.