"I always believed in this group", Holder told Sky Sports.
The total turned out to be considerably below-par as the Windies responded with 427 and 322 for five in their two innings.
Thanks to Hope and Brathwaite's heroics, the West Indies brought themselves level at 1-1 in the series going into the third and final Test at Lord's, which begins on September 7.
This was also, excluding fixtures against Bangladesh and Zimbabwe, just the West Indies fourth Test win away from home in 88 matches spanning 20 years.
And the pair were at it again on day five, adding 144 runs for the third wicket before Brathwaite (95) edged Moeen Ali to slip to leave the tourists on 197-3, 125 adrift of their victory target just before tea.
Blackwood also got a life when Stokes dropped him in the deep but with just six runs needed off nearly as many overs at the time and while Blackwood fell with victory in sight, England's fate was already sealed.
With England having set a formidable target - the Windies started the day needing 317 with all wickets intact - on a turning pitch and under cloud cover, the two young batsmen negotiated their testing examinations superbly.
SCORES: England 258 all out & 490 for 8 declared. England's bowlers toiled, but there was plenty of loose stuff which meant the run rate never got out of hand for Windies.
But Broad did reduce the West Indies from 46 for none to 53 for two.
You wonder whether Kraigg Brathwaite and Shai Hope knew that.
England's captain Joe Root (right) talks to Stuart Broad (left) and James Anderson (centre) during day five.
Shai Hope s single off Broad completed a superb century off 175 balls, including 13 fours, as he became the first West Indian to score hundreds in both innings of a Test in England since Gordon Greenidge at Old Trafford in 1976.
Even though Blackwood was stumped by Jonny Bairstow off the bowling of Moeen, Hope hit the winning runs the very next over and finished unbeaten on 118 off 211 deliveries, which included 14 boundaries. The list of dropped chances was added to when Brathwaite offered a return catch to Broad which he couldn't hold, but the ball deflected into the non-striker's stumps with Hope well out of his ground.