The tourists were already 2-0 down in the series but managed to end on a positive note ahead of the upcoming Twenty20 contests.
Jonny Bairstow (56), captain Eoin Morgan (43) and Ben Stokes (57* from 39) were also notable with their contributions to the target, while Chris Woakes hit 24 from just 19 balls as the 50-over mark approached.
The hosts entered the final over needing 16 runs to win and got off to the perfect start as Jadhav hit successive boundaries with the first two balls, before Woakes produced two dot balls to ensure a nervy finish.
With time running out, Jadhav took a gamble and went for a six, only to find himself caught by Sam Billings on the boundary. Bhuvneshwar Kumar came on hoping to make a memorable cameo for the final ball, but it was not to be as the tourists claimed their first win of the tour.
The three-match T20 series begins in Kanpur on Thursday.