The West Indies, set 200 for the victory on the last day, were down to 27-3 after the double early attack of England’s fast bowler Jofra Archer.
Blackwood, however, remained firm until, ahead of his second century trial, he led England captain Ben Stokes to James Anderson halfway through, with visitors who only needed 11 more tracks to win.
But John Campbell, forced to retire injured at one after being hit on tiptoe by Archer, has returned to hit the winning tracks.
West Indian captain Jason Holder, the most highly rated test all-rounder in the world before Stokes, had not been released.
The game was a personal and tactical triumph for Holder, who scored 6-42 as the best test in the first innings in England 204 after Stokes, leading the team in the absence of Joe Root, won the draw and beaten.
Although they hold the Wisden Trophy, the West Indies have not won a series of tests in England for 32 years.
But this victory brought them 1-0 with two players to play in a series behind closed doors in view of the second Old Trafford Test next week.
It was a deserved success for the West Indies, which continued their tour despite more than 44,000 coronavirus deaths in Britain during the pandemic, but Sunday could have been a different story for England if they had not given Blackwood several reproaches.
The 28-year-old Jamaican was only five when he beat the champion Dom Bess only for Stokes, moving secretly, to miss the chance.
And he had moved to 20 when the wicker keeper Jos Buttler launched a one-handed chance down Stokes’ leg.
Greetings were reported, but Blackwood would have been out if Buttler had held out.
England therefore squandered a possible possibility of exhaustion when Zak Crawley fumbled.
But with the West Indies exactly needing another 100 to win, Archer, born in Barbados, challenged a docile shot to produce a high delivery of 90 miles per hour that Roston Chase, out of 37, could only divert to Buttler with his glove and helmet.
It was the end of a precious stand of 73.
Little Blackwood went on, leading the cover of both Bess and Anderson, England’s foremost test token holder, for two of his dozen borders in a 154-ball inning.
Archer had previously made a profit 23 before being the last man to come out in the second English inning 313.
West Indian fast pitcher Shannon Gabriel took 5-75 in 21.2 over – his sixth five-wicket shot in his 46 rounds.
Archer then reduced the West Indies to 7-2 after being insignificant in the first innings after being selected ahead of the fallen veteran Stuart Broad.
He got Kraigg Brathwaite to play on and he got Shamarh Brooks for a duck.
Shai Hope, whose two hundred Tests scored a victory over England in Headingley three years ago, was later launched by Mark Wood for nine.
But it was England’s loss of five wickets for just 30 runs late Saturday, a slump caused by Holder’s dismissal of Stokes, which proved more important in the end.