Jermaine Blackwood held firm for the West Indies to leave England needing a dramatic final session if they were to win the first Test at Southampton on Sunday.
West Indies were 143-4 at tea on the last day, needing just 57 more runs to reach a victory target of 200 in a match that marks international cricket's return from lockdown.
Blackwood, given several reprieves, was 65 not out, with Shane Dowrich unbeaten on 15.
England fast bowler Jofra Archer had taken two wickets before lunch as West Indies slumped to 27-3.
But Roston Chase (37) and Blackwood frustrated England before Barbados-born quick Archer broke a fourth-wicket stand of 73.
Blackwood, however, had made just five when he edged off-spinner Dom Bess only for England stand-in captain Ben Stokes to move too quickly in anticipation at slip and drop the chance.
And he was given another life on 20 when wicketkeeper Jos Buttler floored a left-handed chance down the legside off Stokes. Leg-byes were signalled but Blackwood would have been out on review had Buttler held on.
England then squandered a possible run-out chance when Zak Crawley fumbled in the first of three-match behind closed doors series.
Blackwood had moved on to 29 when he forced paceman Stokes past Rory Burns in the gully, although this time a review would have revealed a no-ball.
But with West Indies needing exactly 100 more for victory, Archer defied a docile pitch to produce a rearing 90 mph delivery that Chase, on 37, could only divert to Buttler via his glove and helmet.
It was a much-needed breakthrough for England, with Archer and fellow fast bowler Mark Wood having just a combined one for 135 between them in the West Indies' first innings after they were both selected ahead of dropped veteran Stuart Broad.
But Blackwood completed an impressive 80-ball fifty before lofting James Anderson, England's all-time leading Test wicket-taker, for four over mid-off.
Archer had earlier hit a useful 23 before he was last man out in England's second innings 313 after they had lost five wickets for just 30 runs late on Saturday.
West Indies fast bowler Shannon Gabriel took 5-75 in 21.2 overs -- his sixth five-wicket haul in his 46 Tests.
Archer then forced John Campbell to retire hurt on one after his first ball of the innings struck the opener a painful blow on the toe before taking two wickets in quick succession.
He had Kraigg Brathwaite, who top-scored with 65 in West Indies' first innings 318, playing on for four.
And West Indies' 7-1 became 7-2 when Shamarh Brooks was plumb lbw for a duck to Archer.
Shai Hope, whose lone two Test hundreds came in a win over England at Headingley three years ago, was then bowled for nine by Wood's fourth ball of the day.
But England could yet rue being dismissed for just 204 in their first innings after Stokes, leading the side in the absence of Joe Root, won the toss and batted.