It is India's sixth successive ODI series win on home soil.
It took India fewer than 15 overs to chase down that modest target, with Rohit Sharma hammering an unbeaten 63 from 56 balls to seal a nine-wicket victory.
"It was a clinical performance. We were surprised West Indies batted".
Oshane Thomas gained an early success when India replied, bowling Shikhar Dhawan (6) in the second over, but that was as good as it got for Windies.
Jadeja set up the convincing victory after returning figures of 4-34 from his 9.5 overs. Once again all the visitors' hopes relied heavily on the shoulders of Shai Hope, but this time he disappointed by bagging a duck.
Thomas also should have had India captain Virat Kohli on 4 but West Indies captain Jason Holder dropped the catch at first slip.
Young paceman Khaleel Ahmed also made his presence felt for India, with two key strikes including the wicket of Holder.
BCCI's announcement of dropping Dhoni had come after the second ODI between India and West Indies ended in a tie.
So promising across the first three ODIs, West Indies' batting unravelled when a share of the series was still up for grabs. Rovman Powell was promoted to open the innings but he struggled badly and departed for a meager 16 runs for which he took 39 balls.
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"To get runs as captain always gives me confidence".
The final ODI is to be played at the new greenfield stadium in Kerala's Thiruvananthapuram.
The two sides will next contest a three-match T20 series, starting at Kolkata's Eden Gardens on Sunday.
For Windies, skipper Jason Holder was top-scorer with 25 runs while Marlon Samuels scored 24 runs. The Men in Blue dominated the hosts in a six-match series, clinching it 5-1.
UMPIRES: C. Shamshuddin (India) and P. Wilson (Australia).
Kohli responded by bringing on Ravindra Jadeja.
MAN-OF-THE-SERIES: Virat Kohli.
FOURTH MATCH: Mumbai, India won by 224 runs.