In the third session, Kohli and Rahane stitched a 105-run stand to take the team past 300.
India have won the toss and elected to bat.
Shaw is the fourth-youngest global batsman to score a century on debut.
Shaw also confessed that he was initially a bit nervous on meeting the senior team players, but Team India coach Ravi Shastri and skipper Kohli comforted him by saying there is nothing like senior or junior here. As he scored his century on the 99th ball of his innings, Shaw became the first Indian to score centuries on his Ranji Trophy, Duleep Trophy and Test debut. He is the 293rd cricketer to represent India in Test cricket and at the age of 18 years 329 days Shaw became India's second youngest opener after Vijay Mehra, who was 17 years 265 days at Bombay's Brabourne Stadium against the Kiwis in Dec 1955.
Already set back by the loss of seasoned new-ball bowler Kemar Roach who returned to Barbados last week due to the death of his grandmother, West Indies suffered yet another blow when captain Jason Holder was ruled out of the match with an ankle injury. Both Pujara and Shaw did not allow leg-spinner Devendra Bishoo or off-spinner Roston Chase to settle in and pounced on every bad delivery.
India's Prithvi Shaw celebrates after scoring fifty runs on the first day of the first cricket test against West Indies.
One can not speak of the future but this 134 off 154 balls, he has done all the right things to book a flight to Australia for the Test series, that starts on December 6 at Adelaide.
Gabriel was clocking in the higher 140kph but that did not faze Shaw.
The Mumbaikar came out with a positive intent and dominated the West Indian bowlers as if he has been there for the longest of times. The right-hander reviewed in desperation but replays showed the ball hitting middle stump.
He got more aggressive in Paul's following over, hitting him for three fours as the pacer was duly punished for bowling far too many looseners.
KL Rahul will be opening the innings. Following the debacle in England, a two-match Test series against West Indies at home, which starts at Rajkot, is perhaps the ideal way to get back in the groove for the Virat Kohli-led Indian team. If the visitors harbor any hopes of coming close to India.