Shaw, just 18, made his global debut on in the ongoing first Test between India and the Windies.
Along the way, Shaw had also become the youngest Indian to score a half-century on Test debut.
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.
On 232 for three at tea, India subdued the Windies in the final session thanks to a 105-run, fourth-wicket stand between the enterprising Kohli and Rahane.
Shaw, at 18 years and 329 days, reached the historic three-figure mark off just 99 balls at the Saurashtra Cricket Association Stadium.
Kohli called his side in a ball after Jadeja completed his maiden Test ton against a Windies attack missing Kemar Roach due to a family bereavement and captain Jason Holder through an ankle injury.
RBI keeps repo rate unchanged at 6.5%
Repo rate is the rate at which the RBI lends money to banks and is an important tool for RBI to control inflation. The Indian rupee is the worst performing Asian currency this year, having lost more than 13 per cent.
He becomes India's second youngest century-maker after Sachin Tendulkar, who in 1990 was 17 years and 107 days when he scored 119 not out against in England in Manchester, but that was in his ninth Test match.
In England, he remained unbeaten on 86 as he ran out of partners.
Day 1 report: India dominated the proceedings on the opening day of the first Test against the West Indies as the hosts posted 364/4 at stumps, thanks to a brilliant show by opener Prithvi Shaw, here on Thursday.
Kohli was all smiles when young Shaw raised his bat after reaching the milestone. He did the same to Devendra Bishoo in the following over.
A second Test hundred in his fourth Test was for the taking but Pant, attempting another six over mid-wicket, failed to pick the googly and top-edged it for a simple catch to Keemo Paul at backward point.