Despite his side's struggles in the longest format in recent years, Holder believed such performances were always within West Indies capabilities, and hailed the victory as just rewards for some previously unheralded toil.
Although none of them went on to dominate the innings with a century, the English batsmen put together a series of partnerships to fight back from a 169-run first innings deficit, and from 94-3 early in their second innings.
Victory saw West Indies level the three-match series at 1-1 as they recorded their first Test win in England since 2000.
England wrestled control of the second test away from the West Indies late on the fourth day on Monday, declaring its second innings on 490-8 and setting the tourists a tough target of 322 to win. "I m just pleased to get the win".
The opener pressed on to register his fifty off 98 balls with seven fours, Shai Hope reaching the same milestone in 28 few balls as England's frustration grew. "(He's got) plenty of courage, plenty of character and plenty of determination". Thus setting Windies 322 runs to win.
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He had Kieran Powell (23) fending to Ben Stokes at fourth slip and then ran out Kyle Hope for the unluckiest of ducks when he dropped a return catch from a Brathwaite drive, only to deflect the ball onto the stumps at the bowler s end as the non-striker backed up.
England captain Joe Root, who bemoaned a day of dropped catches, described Hope's knock as "exceptional".
Hope took the bulk of the plaudits after becoming the first man ever to make two tons in a first-class game at Headingley.
When Hope did offer a chance, slashing at Broad on 106, Cook could not hold on to the rapid chance and the batsman rubbed salt in the wound by upper-cutting the seamer for six. Appropriately, it was Hope who struck the winning runs with a legside flick for two off Chris Woakes.
Stuart Broad had a hand in both wickets to fall on the final morning at Headingley - literally in the case of a weird run out of Kyle Hope - but Kraigg Brathwaite escaped two dropped catches to continue his outstanding match.
"(Hope) played exceptionally well - on the fifth day, against high-quality bowling, it was a great knock", said Root, whose two fifties in the match were eclipsed by Brathwaite and Hope.