Jaiswal hit 22 fours in his fifth 150-plus score in tests to show why he is one of the world's most exciting batsmen.
India captain Shubman Gill was batting on 20 at stumps and would be pleased at how his batters vindicated his decision to bat first in the bid to secure a 2-0 series sweep.
It was the first time Gill had won the toss since taking over as India test captain earlier this year.
KL Rahul (38) survived a close lbw appeal but Jaiswal was rock solid during their opening stand of 58.
Touring captain Roston Chase opted for spin from both ends and harnessed Jomel Warrican with Khary Pierre.
Warrican lured Rahul out of the crease with his third delivery and spun it past the bat. Wicketkeeper Tevin Imlach, one of two new faces in the West Indies playing XI, had all the time in the world to whip off the bails.
Jaiswal reached his fifty in the first over after lunch when he hit Jayden Seales for three fours and brought up his seventh test hundred, taking two off Pierre's bowling.
The 23-year-old removed his gloves and helmet, made a heart sign and blew kisses in celebration.
Questions have been raised about whether B Sai Sudharsan has what it takes to succeed in the crucial number three slot, but the left-hander responded in style with a fluent 87.
West Indies did not help their cause either by dropping Sudharsan when the batter was on 58.
Sudharsan offered a leading edge towards short mid-wicket where Warrican dived to his right but the ball jumped out of his cupped hands, leaving bowler Justin Greaves crouching mid-pitch with his head in his hands.
Sudharsan looked primed for a maiden test hundred, but Warrican dismissed him lbw to end the batter's 193-run partnership with Jaiswal.
Sudharsan reviewed the decision but could not get it overturned and left after hitting 12 fours in his second half-century in eight innings.
Jaiswal then drove and cut with elan to inch closer to a third test double hundred.