After declaring on their overnight total of 448-5, a lead of 286, the Windies fared no better in the second innings with the bat as they were dismissed for a paltry 146 in the second session.
Having scored an unbeaten 104, Jadeja showed his allround star quality with figures of 4-54 in 13 overs while fellow seamer Mohammed Siraj took 3-31 in 11 overs.
Alick Athanaze top-scored for the Windies with 38 while Justin Greaves struck 25 but the Caribbean outfit only lasted 45.1 overs at the crease.
It was almost identical to the first innings of the Test when they were bowled out for 162 in 44.1 overs.
The West Indies will need to improve drastically to have hope of salvaging something from the series with the final Test set to start in Delhi next Friday.
India regained the lead in their five-match T20 international series against the West Indies after Abhishek Sharma's explosive half-century and a disciplined bowling performance secured a 14-run victory in Indore on Sunday.
Shai Hope continued his fine form with an unbeaten century as West Indies pulled off their highest-ever T20I run-chase to beat India by six wickets and level the five-match series at 1-1.
Bhuvneshwar Kumar could be in line to make his first international appearance in four years after recalled to the India squad for the T20I series in New Zealand starting later this month.
Shreyas Iyer struck his maiden T20I century as India thrashed the West Indies by eight wickets with more than five overs to spare in the first game of the five-match series in Lucknow on Tuesday.
