At tea the hosts were 70 for three in pursuit of 192, with a 1-1 series draw the carrot dangling in front of them.
But on a pitch that has favoured bowlers throughout, England were buoyed by Stuart Broad’s dismissal of Marlon Samuels late in the afternoon session.
Chris Jordan had earlier played a part in removing both openers, trapping Shai Hope lbw and snaffling Kraigg Brathwaite with another memorable catch off Moeen Ali.
The West Indies had earlier set up the game by dismissing the tourists for 123, taking the final five wickets for 84 runs before lunch.
After surviving one awkward over before the break, Brathwaite and debutant Hope made a useful opening stand of 35.
Brathwaite (25) did most of the scoring through relatively safe strokes but Hope was dropped on four when Broad drew him into the drive. The chance flew to Joe Root at wide third slip but he could not cling on, diving to his left.
More worryingly for England, they then burned both of their DRS reviews in the space of 11 balls.
A sceptical Alastair Cook was persuaded by Jonathan Trott to refer a caught behind decision against Brathwaite, but it was a misguided intervention.
Jordan was then certain he had Hope lbw but umpire Billy Bowden was unmoved and his verdict was upheld by a small margin. But Jordan was not to be deterred, playing a key role as both openers fell with the score on 35.
First he trapped Hope lbw in front of leg stump then, four balls later, he produced his fourth superb one-handed catch of the series.
Moeen found Brathwaite’s edge with his fifth ball before Jordan pulled off his party piece, transferring his weight in the wrong direction at slip before throwing out his left hand to snatch the ball out of the air.
Samuels and Darren Bravo halted the surge, seeing out Jordan’s disciplined spell and making sure not to miss out when Moeen dropped short.
The pair put on 35 before Broad and Root dried up the runs with 22 consecutive dot balls.
The 23rd brought the wicket, Broad upping his pace and slanting one through Samuels’ defence and into the stumps.
England had resumed on a fragile overnight score of 39 for five and added 23 more runs before Gary Ballance pushed at Veerasammy Permaul’s second ball of the morning.
Ben Stokes and Jos Buttler then put on 33 at a damaging rate of more than four an over.
Had they been allowed to continue picking gaps in the field they could have taken the game away but Stokes gave it away on 32, advancing to Permaul and popping a leading edge to extra cover. Buttler, who got off the mark with a crunching six, was in need of further support but Jason Holder conjured a dramatic double strike to leave England 98 for nine.
Jordan was first to fall, on the wrong side of a fractional lbw decision and Bowden’s crooked trigger finger.
But there was no doubt about Holder’s next ball, a vicious yorker that caught Broad cold and ripped out off stump.
James Anderson survived the hat-trick ball and kept Buttler company in a valuable partnership worth 25.
Buttler was going through the gears, taking Shannon Gabriel for four and a steepling six to reach 35, but left his partner at the mercy of the returning Taylor.
The seamer needed just one ball to win the battle, going full and fast and winning an lbw on review following another curious Bowden decision.