Jaiswal was 173 not out at the close, his seventh Test hundred, while Sai Sudharsan struck 87 as the home team ended the day on a total of 318-2.
After India captain Shubman Gill had won the toss and opted to bat, Jaiswal and KL Rahul put on a 58-run opening stand before Rahul was undone by left-arm spinner Jomel Warrican to be stumped for 38.
Sudharsan then joined Jaiswal and the two left-handed batters took control as they combined for a mammoth 196-run partnership.
Sudharsan would have been disappointed as he did not convert his ssocre to a maiden Test century after being trapped lbw to Warrican for 87.
Jaiswal and Gill then buried down the hatches in the final session for an unbeaten 67-run stand with the home skipper set to resume on 20.
India lead the two-match 1-0 after a convincing victory inside three days in the opening match in Ahmedabad.
India wrapped up a dominant 2-0 series win over the West Indies after cruising to a seven-wicket triumph in the second and final Test at New Delhi's Arun Jaitley Stadium on Tuesday.
India are on the cusp of sealing a 2-0 series victory, but it was not without plenty of steely resolve with the bat from a stoic West Indies line-up in Delhi on Monday.
Australia captain Alyssa Healy struck a superb century to guide her team to a three-wicket win against India at the ICC Women's World Cup in what was a record run-chase.
India took control of the second Test against West Indies thanks to a five-wicket haul from Kuldeep Yadav on day three at the Arun Jaitley Stadium on Sunday.
