Jadeja, who was named man-of-the-match, polished off the West Indies' tail and India did not need the customary break after end of the first innings to get past their target.
Skipper Jason Holder top-scored with 25 to raise hopes of a West Indies fightback but the rest of the batting folded.
Rohit Sharma, 63 not out, and Kohli, 33 not out, made good on their stupendous form through this series, grinding out the visitors' bowling attack with a 99-run partnership for the second wicket off 78 balls.
After the resounding victory in the fourth One-day International (ODI) at the Brabourne Stadium in Mumbai, the Virat Kohli-led hosts lead the series 2-1, with the second match being tied.
The tourists also included an extra fast bowler in Oshane Thomas, who took the place of opening batsman Chandrapaul Hemraj.More news: German Markets Hint at Austerity Easing Across EU on Merkel Exit
Powell's loose drive off a wide delivery from Bhuvneshwar Kumar ended in the gloves of wicketkeeper Mahendra Singh Dhoni, while Hope was bowled after he played on attempting an expansive cover drive off Jasprit Bumrah.
Jadeja also trapped big-hitter Shimron Hetmyer lbw for nine to rattle the West Indies middle-order.
Jadeja was the pick of the bowlers ending with 4-34 while there were two wickets apiece for Bumrah (2-11) and Ahmed (2-29). Captain Kohli was at his dominant best as he slammed 558 runs in the series, which is his most in a bilateral ODI series. "It won't happen all the time, but when I'm going, I want to keep going longer", said Kohli.
The Indian side hopped across to England, and after clinching the three-match T20I series, they started the ODIs with a bang by winning the first match easily. The match will kickstart at 1:30 hrs IST.
In what was scheduled to be a day/night contest, India wrapped up the match well before dark after dismissing the Windies for 104 in 31.5 overs.