Chasing a daunting target of 459, the tourists were all out for 250 in 100.3 overs as India wrapped up victory just before tea on the fifth and final day.
Resuming on 103-3, the tourists got off to a poor start when Shakib Al Hasan was caught at short leg off Jadeja for 22 in the third over of the morning and first-innings centurion Mushfiqur Rahim departed for 23.
The tourists reached 202-5 at lunch but lost their five remaining wickets after the interval to concede defeat.
Mahmudullah and Sabbir Rahman added 51 for the sixth wicket but both fell to Ishant Sharma, and India's bowlers mopped up the tail to clinch a sixth successive series win and stretch the team's unbeaten streak to 19 matches.
Up next for India is a four-Test series against Australia which begins on February 23 in Pune.