England was 284-8 in the second inning at the end of the fourth day, a 170 point lead in a game that marks the return of international cricket from the blockade.
England reacted during a fourth wicket pair of 98 between Zak Crawley and Stokes.
But their 249-4 was soon turned into 279-8 when five wickets fell for just 30 runs in the last hour.
As soon as Stokes fell, Crawley was then captured and thrown by paceman Joseph for a Test-best 76.
Suddenly, England’s two batsmen at the fold – Papa and Jos Buttler – both failed.
Buttler, who overturned to Holder by five, fell by nine when he crossed a huge space between Joseph’s bat and pad.
The World Cup winner wicketkeeper Buttler has now made only one hundred in his 42 trials.
And there was still time before closing for Shannon Gabriel’s fast spearhead (3-62) to launch both Dom Bess and Ollie Pope.
England was still behind the first West Indian innings 318 when Crawley hit the fold.
But the 22-year-old, in his fifth test, completed a well-done 50-year-old when he swept the spinner Roston Chase offside for four.
Poor first innings
Crawley, who now faces the new ball, passed his previous best 66 test against South Africa in Johannesburg in January.
Stokes, jumping to the side in the absence of Joe Root, continued to lead the lead by driving Gabriel four.
The handyman had already scored the highest with 43 in England’s first inning wizards 204 before the paceman was the homeowners’ attack choice with 4-49.
But for the second time in the game he fell on Holder.
The gigantic West Indian paceman squared Stokes and had him captured by Shai Hope, skillfully positioned as the finest of two men in the gully for the left-handed batter.
It was a tactical and personal triumph for Holder, ranked ahead of Stokes as the world leader in all-round tests.
There was more joy for the Windies when Crawley, aiming for the side, was captured and launched by Joseph.
England bounced back 15-0 in the first of a three-door series behind closed doors.
Despite being a batting handyman, Chase had made the best 8-60 test when the West Indies beat England in his Barbados homeland last year on the way to a 2-1 streak win.
Chase made the initial turn on Saturday when Rory Burns (42) carelessly cut it.
Dozer Dom Sibley made a scrupulous fifty 161 balls.
Subsequent delivery saw Sibley play Gabriel only for the third referee Michael Gough to rule the bowler who had been guilty of a marginal no-ball.
But, two balls later, Sibley – still in 50th – glanced at Gabriel on Dowrich as he was again caught on the ground in his fledgling Test career.
Joe Denly, potentially competing for a place with Sibley when Root returns after the birth of his daughter for next week’s second test at Old Trafford, needed a high score to take an average of low level tests of less than 30 years.
But instead he fell tamamente for 29 when he chipped Chase a Holder in short midfield.
The West Indies have been on top for most of this game, with Holder passing Test 6-42 after losing the draw.
Kraigg Brathwaite then made 65, the first fifty test at the opening of 22 innings and Dowrich 61 while tourists established a valuable 114 innings advantage.