Kohli, who started on his overnight score of 72, got to his hundred in his 123rd innings with a boundary off leg-spinner Devendra Bishoo.
However, Prithvi Shaw stitched a 206-run stand alongside Cheteshwar Pujara before Pujara fell for 86.
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At 18 years and 329 days, Shaw reached the milestone off just 99 balls, adding to a host of records he holds in his blossoming career. Earlier in the same year, Shaw had also scored a hundred on his Ranji Trophy debut. He soon got to his half-century and went to lunch just 20 odd away from a dream start to his Test and global career.
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. Gabriel trapped his opening partner Rahul in front with a sharp incoming delivery to give the West Indies an early breakthrough.
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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. The right-hander reviewed in desperation but replays showed the ball hitting middle stump.
Kraigg Brathwaite, who is standing as captain after Jason Holder suffered a last-minute ankle injury, juggled his bowlers who often looked toothless.
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Once Shikhar Dhawan was left out of the two-Test series against West Indies, the path was clear for Shaw to make his debut.