Skipper Virat Kohli, who was all smiles when young Shaw raised his bat after reaching the milestone, was at the crease on 4 with vice-captain Ajinkya Rahane (batting 0) with Shaw offering an easy return catch to leggie Devendra Bishoo trying to play against the turn.
In the morning, Shaw, who became the 293rd cricketer to represent India in Tests, showed supreme confidence from ball one, on which he offered a watchful leave.
West Indies improved its lines post lunch, but it didn't hamper Shaw, who reached his century off 99 balls, the third quickest on debut in test history.
There is plenty of excitement around the two-Test series despite India starting as the overwhelming favourites to complete a whitewash of the West Indies, thanks to some bold selection calls from the host nation.
Shaw wasted little time in picking up where he had left off in the first session, twice drilling leg-spinner Devendra Bishoo to the leg side boundary in the first over after the interval.
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.
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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.
Gabriel was clocking in the higher 140kph but that did not faze Shaw. West Indies looked pale and exhausted on most occasions.
While Shaw punched and drove effortlessly off pacers, he was equally comfortable against the spin duo of Bishoo and Chase. He also produced a delightful straight drive on way to reaching his half-century which came off 56 balls. If the visitors harbor any hopes of coming close to India. 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.
India will look to maintain their status in the ICC Test rankings during the two-match Test series against the West Indies.