The diminutive right-hander becomes India's second youngest century-maker after Sachin Tendulkar, who in 1990 was 17 years and 112 days when he made 119 not out against in England in Manchester during his ninth Test appearance.
With hundreds on debut in Ranji trophy, Duleep trophy and Irani Trophy, all eyes were on Prithvi after it was announced he is set to make his debut in the first Test match. Shaw (134 off 154) and Cheteshwar Pujara (86 off 130) laid the foundation for a big score with a 206-run partnership after the early loss of K L Rahul (0).
Shaw led India's fightback after they lost opener Lokesh Rahul for nought in the very first over off Shannon Gabriel.
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.
In the last one year, Shaw has been sensational and has forced his way into the Indian Test team by performing exceptionally well in the domestic circuit and for India A. The Mumbai batsman has a first class average of 56.72 at a strike rate of 76.69.
Shaw is the seventh-youngest worldwide batsman to score his first Test century.
Kohli and Pant, 19 not out, handled the attack to stumps on day one of the first test.
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. Second ball is pitched on leg which Kohli nicely turns towards the fine leg boundary.
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.
With tea beckoning, West Indies struck twice to temporarily stall India's progress. Ajinkya Rahane contributed 41 runs. Kemar Roach returned home for the funeral of his grandmother, and captain Jason Holder withdrew because of an ankle injury.
Rahane, meanwhile, had faced 92 balls and struck five fours and looked a safe bet for a half-century before edging a cut at part-time off-spinner Roston Chase to be caught at the wicket, with the close in sight.