With the achievement, Shaw became the fourth youngest player to score a hundred on debut and the youngest ever Indian.
Prithvi Shaw becomes the second youngest Indian to score a maiden test ton after the legendary Sachin Tendulkar.
Last Indian to achieve this feat was Rohit Sharma, also against West Indies in 2013.
Prithvi Shaw scored at better than a run a ball before lunch on his test debut in Rajkot.
India opener Lokesh Rahul was out in the first over for a duck, but Shaw and Pujara cruised, putting on 206 runs together. Gabriel trapped his opening partner Rahul in front with a sharp incoming delivery to give the West Indies an early breakthrough. Holder injured his ankle during the preparatory camp in Dubai, and in his absence, opener Kraigg Brathwaite was handed over the captaincy for the second time in Tests. Unfortunately, Shaw fell at the stroke of tea, in what was a soft dismissal as he chipped one straight into the hands of leggie Devendra Bishoo.
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India cashed in on the weakened attack by scoring quickly and already, the Windies face a long road back into the match, heading into Friday's day two.
Shaw, who was 75 not out at lunch, reached the three figures in the afternoon session with a typical punch to the cover, the same way he got his first runs in worldwide cricket.
Cheteshwar Pujara too looked at ease at the other end and was on 74 off 100 balls when the Shaw's century came.
Shaw reached his hundred off just 99 deliveries in the second session on day one..
Kohli, who is the world's number one Test batsman, got to his half-century against Bishoo and was getting more unsafe with each passing ball.
Shaw's innings was studded with 19 fours while Pujara hit 14 boundaries before poking at a length ball half-heartedly to wicketkeeper Shane Dowrich off pacer Sherman Lewis, who bagged his first Test scalp.