The Australian received a 12-month ban for his part in the ball tampering controversy during the Cape Town Test and can not officially return to playing state, Big Bash and national level cricket until March 29 next year.
Skipper Virat Kohli on 72 and R.R.Pant with 17 remained unbeaten when the stumps were drawn. Unfortunately, Shaw fell at the stroke of tea, in what was a soft dismissal as he chipped one straight into the hands of leggie Devendra Bishoo.
Kohli reached his 20th test half-century off 100 balls.
RAJKOT: Indian cricket has a new star after Prithvi Shaw became the country's youngest batsman to score a century on debut during Thursday's Test against the West Indies.
Electing to bat, India were 364 for 4 at stumps.
Shaw became India's second-youngest century maker after Sachin Tendulkar as he reached three figures early in the second session. Rahul reviewed the decision only to lose his wicket to Shannon and a review.
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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.
Shaw is the fourth-youngest global batsman to score a century on debut.
India opener Lokesh Rahul was out in the first over for a duck, but Shaw and Pujara cruised, putting on 206 runs together. But, Sherman Lewis managed to get the much-needed breakthrough as Pujara edged one to the bowler for a well-made 86 when India's score had surpassed the 200-run mark.
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.
Kohli and Ajinkya Rahane, who made 41, took over from Shaw with a patient 105-run partnership despite West Indies bowlers keeping a tidy line and length to check the flow of runs in the final session of play. Rahane tried to cut a Roston Chase's delivery skidding away from him and in the process got too far leg side of that to middle it giving wicketkeeper a simple catch.