Barring pacer Shanon Gabriel (1/66), none of the bowlers troubled the Indian batsmen on a greenish surface which did not seem to do much.
Tendulkar was 17 years and 107 days old while Shaw is 18 years and 329 days old when he got to his century. The World Cup-winning U19 captain was handed his maiden Test cap by the skipper Virat Kohli on Thursday morning, after which he opened the batting for India along with KL Rahul.
More than half of his runs came through boundaries, 19 in total. Subsequently, Shaw offered an easy return catch to leggie Devendra Bishoo trying to play against the turn.
He was not facing one of the best attacks but he gave ample evidence of his brilliance on way to a memorable hundred.
Pujara also played an uncharacteristically quick knock as he brought up fifty off 67 deliveries, but missed out on his hundred after being caught behind off debutant paceman Sherman Lewis.
Rahul was gone for a golden duck when Caribbean pacer Shannon Gabriel trapped the Indian opener in front of the wickets. The right-hander reviewed in desperation but replays showed the ball hitting middle stump.
India lost a wicket in the very first over but then Pujara and Shaw scored 206 for the second wicket.
The teenage prodigy collected two fours off Bishoo in the 11th over and did the same to Chase in the 20th over.
Shaw reached his hundred off just 99 deliveries in the second session on day one..
The West Indians looked listless on the field as boundaries came at will for India.
When India announced a 15-member squad for the two Tests, it was clear that the management was looking at this series as a preparatory pad for the upcoming Australia tour.