At 18 years and 329 days, Prithvi Shaw became the youngest Indian and the fourth-youngest overall to score a century on Test debut, against the Windies in Rajkot on Thursday (4 October). Skipper Virat Kohli also hit a landmark ton, top-scoring with 139.
Shaw also became the second youngest Indian after Sachin Tendulkar to score a Test century.
Earlier, Opting to bat, the hosts lost K.L. Rahul for a duck in the very first over of the two-match series as Caribbean pacer Shannon Gabriel caught the Indian opener in front of the wickets.
The last session saw India maintain a good run rate with Kohli and Rahane (41) stitching a 105-run partnership and helping India get past the 300-run mark.
The 18-year-old didn't disappoint and lived up to the expectations as he became the youngest Indian to score a Test century on debut.
Pujara, who is inching closer to 5,000 Test runs, ensured India a solid start with Shaw, smashed 14 boundaries.
The West Indies handed a big setback even before toss with the last-minute withdrawal of captain Jason Holder, looked ordinary at best on the field.
Shaw has now scored a century each on his Ranji Trophy debut - 120 vs Tamil Nadu at Rajkot, Duleep Trophy debut - 154 vs India Blue in Lucknow and Test debut.
Shaw, who was 75 not out at lunch, reached the three figures in the afternoon session with a typical punch to the cover, the same way he got his first runs in worldwide cricket. 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. "Continue batting fearlessly", Tendulkar said on Twitter.
Rishabh Pant (17) and skipper Virat Kohli (72) were at the crease when umpires dislodged the bails for the day.