The opposition attack was far from threatening but due credit must be given to Shaw, who batted like a seasoned campaigner in his first match for India.
Indian skipper Virat Kohli on Friday hit his 24th Test Century and surpassed former Australian skipper Steve Smith (23) to record the most number of Test hundreds by an active player.
In the second session, Shaw (134) slammed a brilliant ton as he became the youngest Indian to score a Test century on debut as India posted 232/3.
The right-handed Shaw struck 19 fours off 154 deliveries while Pujara, also right-handed, faced 130 balls and counted 14 fours in chalking up his 19th half-century in his 63rd Test.
Virat Kohli also surpassed Virender Sehwag (714 in 2009-10) to score the most number runs in five consecutive Test innings in India.
On 232 for three at tea, India subdued the Windies in the final session thanks to a 105-run, fourth-wicket stand between the enterprising Kohli and Rahane.
He put on a 206 run partnership with Cheteshwar Pujara for the second wicket.
While Shaw is making his India debut, Sunil Ambris and Sherman Lewis will also make their global debut for West Indies.
And Shaw finally departed in the final over before the break when he tamely chipped a return catch to Bishoo. He drives one through the covers to bring up his hundred.
While India lost KL Rahul (and a review) in the first over after Shannon Gabriel trapped him before the stumps, Shaw and the local lad, Pujara, steadied the ship and disallowed West Indies any more wickets till lunch. After Rahul's dismissal, Shaw and Pujara gave the innings a move on and did not look in any sort of trouble.
Shaw, however, continued batting with confidence and his first boundary came in the second over bowled by Keemo Paul, another back foot punch towards the point boundary. Their troubles had mounted even before the start of the game as Holder pulled out with an ankle injury, giving Kraigg Brathwaite a chance to lead the team.