The hard-fought victory was sealed by a special catch from Ollie Pope on short leg as he dived full stretch to complete the remarkable grab on the rebound on the first ball following the umpire's signal for the last hour of play.
Kemar Roach was the final batsman to be dismissed as off-spinner Dom Bess found a way to crawl through his dead-bat approach to defending every delivery.
West Indies entered the third session in pursuit of the improbable 312-run target with five wickets in hand and the realistic goal of batting out the remaining overs.
However, they soon found themselves sliding into disarray when Shane Dowrich got out in identical fashion to his dismissal in the first innings.
The diminutive wicketkeeper-batsman shuffled across the stumps and missed a flick off the bowling of Chris Woakes prompting the umpire to raise his finger in reaction to the lbw appeal.
The review opted by the batsman returned umpire's call as the ball barely clipped the stumps in its trajectory leaving a dejected Dowrich making his way back to the pavilion for his second duck of the match.
West Indies skipper Jason Holder then stitched a steady partnership with top-scorer Shamarh Brooks with both batsmen showing a fair bit of control in their stroke play during their time out in the middle.
Brooks eventually departed for a 136-ball 62 just when the visitors began to believe in salvaging a likely draw.
The 31-year-old was trapped in front of the stumps from a Sam Curran delivery that sharply jagged back in and caught the batter on the crease.
Holder briefly continued his resistance and asserted his dominance on the proceedings with a couple of imperious shots off Bess including a mighty loft down the ground for a massive six.
Two balls after the maximum, Holder was undone by a ripper from Bess as the spinner had his revenge by finding the gap between the bat and pad and rattling the opposition captain's stumps.
Earlier in the post-lunch session, Ben Stokes proved his status as England's designated partnership-breaker once again when Jermaine Blackwood walked into the all-rounder's trap of the bodyline tactic.
Blackwood was peppered with an excessive dosage of short balls from Stokes before one viciously leapt towards the batter's rib cage and caught his glove only to be caught by a diving Jos Buttler.
His dismissal meant West Indies lost their first wicket following a 100-run stand between Blackwood and Brooks after a top-order collapse triggered by Stuart Broad's new-ball burst left them 37-4.
Shai Hope's nightmare run in Tests stretched to another failure as Broad's brutal in-swinger cut him in half. Hope has now gone 37 Test innings with only two fifties to show in his mediocre record in the longer format.
England's day started on a high with Stokes bringing out his white-ball batting prowess by depositing three sixes and four boundaries in his unbeaten 57-ball 78.
Batting with the fielders all scattered around and protecting the fences, Stokes launched meaty hits deep into the stands as he hastily built England's towering lead.
Joe Root was the only England player to get out in the morning when he sacrificed his wicket in a misjudged run as the hosts raced to 129-3 declared in 19 overs.
Stokes' tally of 254 runs and three wickets in the match ensured that he took home the man-of-the-match prize as his stats in the series have reached otherworldly levels of brilliance.
The two teams will renew their rivalry for the series-deciding match at Old Trafford this weekend on July 24.