Having lost the Test series 2-1 and drawn the one-day leg, a 3-0 triumph allows England to end a tricky tour on a high while their opponents have had the look of disinterested participants in two woeful outings at Warner Park.
England were invited to bowl first and Willey was in business instantly, tossing the first delivery of the day up outside off stump and inviting Shai Hope to drive.
The opener obliged but only half-committed to the stroke and pinged a gentle catch to Alex Hales at cover, setting the tone for another dismal day. Willey doubled down when Shimron Hetmyer failed to clear Chris Jordan at mid-off and turned a bright start into a golden one as he struck twice in his third over.
Debutant John Campbell, picked in place of the rested Chris Gayle, got himself in an ugly position and slogged high in the air, with Joe Denly watching the skier carefully and hanging on at point.
Two balls later it was Darren Bravo's turn, nibbling at one outside off stump and angling a low catch to Bairstow's left. After three overs Willey boasted personal best figures of four for seven but was shuffled out of the attack before he could chase England's first five-wicket haul in T20 cricket.
The 29-year-old might have fancied his chances of adding one more at the death but the Windies never even threatened to last that long. Jason Holder, over-promoted at number six, greeted Denly's leg-spin by launcing the first six of the day but fell next ball attempting another big hit.
Jordan was the man underneath it but it was a straightforward chance compared to the blinder he pulled off next over. Nicholas Pooran can consider himself unfortunate, having connected powerfully with a pull shot that could easily have ended up on the grass bank.
Jordan had other ideas, tracking the flight as he raced round the boundary edge and plucked the ball out of thin air for the latest in his catalogue of breathtaking catches. The scoreboard read 48 for six and England finished the job clinically for the addition of another 23 runs.
Wood's pace was too hot for the tail as he finished with three for nine, Carlos Brathwaite's thick outside edge brilliantly intercepted by Bairstow's right glove and Sheldon Cottrell bowled as he scuttled away to leg.
There was just enough time for Rashid to join the fun, summoning a pair of googlies that left Fabian Allen and Obed McCoy categorically outclassed.
Alex Hales gave England's chase a jump start, pounding two fours and a six over long on in Cottrell's opening over. There was another boundary off Holder before the home skipper sent him on his way for 20, averting the prospect of an ignominious 10-wicket loss.
Bairstow picked up the baton, deciding not to linger over the job at hand and riding one life on 19, when Hetmyer fumbled a full-blooded pull. He took a liking to Allen's innocuous spin, middling three boundaries and a six off the all-rounder as well as flogging Holder over long leg.
There were still 12 needed when he was cleaned up by Devendra Bishoo's leg-break but captain Eoin Morgan ensured the win came in record time, finishing things just after the scheduled halfway with six and four off Bishoo.