The second and third Tests will be held in Manchester.
Replying to the hosts' first innings of 204, West Indies marched to 318 all out, to secure a 114-run advantage and remain in control heading into today's critical penultimate day of the contest at the Ageas Bowl.
England lead by 170 runs after finishing on 284/8 at stumps.
The picture had changed rapidly, with England's 139-run lead suddenly looking far thinner than it had just minutes before.
No sooner had stand-in England skipper Stokes (46) fallen to rival all-rounder Holder for the second time in the match then Crawley was caught and bowled by paceman Alzarri Joseph for a Test-best 76.
Joseph was also impressive, taking 2-40 off 16 overs. Jos Buttler (9) then played on off Joseph after which Shannon Gabriel took Dom Bess (3) and Ollie Pope (5).
In a stunning development, English fast bowler Stuart Broad has publicly expressed his displeasure over the team's decision to leave him out from the playing XI against West Indies in the first Test.
Without Broad, they opted to bat first in grey, damp conditions that are likely to have suited his bowling, instead bowling last on a pitch they hoped would wear enough to suit Archer and Wood.
"If we bat for five hours tomorrow to chase 180-190 it´s a normal batting day, not a chase where you have to go at it".
"They bowled quite well but the pitch was offering a bit of up and down bounce and we've definitely got the bowlers to take 10 wickets on there".
None of what followed should take away from Crawley's efforts, with the 22-year-old showing maturity beyond both his years and his five global caps to produce the highest score of the match amid high tension.
Watch day five of the first #raisethebat Test between England and West Indies live on Sky Sports Cricket from 10.30am on Sunday. By the end of the session, they had one review left in the innings. "I didn´t expect anything different".
With the England attack proving ineffective, West Indies safely navigated the first hour before losing Hope three deliveries after the drinks break, when he edged an ambitious drive at Bess for Stokes at first slip to snare an easy catch at 102 for two. Their stand lasted until Burns sliced a long hop from Roston Chase to John Campbell at point- a tame dismissal undoing all his hard work.
Dom Sibley, Burns´ opening partner, made a painstaking fifty.
The Trinidadian was visibly aghast but he returned to his mark and finished the job two balls later, with Sibley caught down the leg side in an increasingly familiar fashion.
But this victory put them 1-0 up with two to play in a behind closed doors series ahead of next week's second Test at Old Trafford.
Blackwood and Jason Holder carried on till West Indies were 11 away. But Blackwood led a middle order recovery along with Roston Chase (37), and then Shane Dowrich (20).
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