An intense affirmation from skipper Joe Root, who arrived at his 24th Test hundred AM meeting, allowed Britain the opportunity to push for a far-fetched triumph.
His side took four wickets for eight runs either side of tea to support their expectations, spinner Jack Filter asserting 3-57 on a dormant pitch.
Yet, West Indies, who didn't endeavor to pursue their objective of 286 out of 71 overs, were steadied by a difficult, solid stand of 80 between first-innings centurion Nkrumah Bonner and all-rounder Jason Holder, which endured 35.5 overs.
Vitally Britain didn't audit a lbw offer against Holder with 22 overs left. Had they done as such he would have been excused by Filter.
Rather he finished 37 not out and Bonner unbeaten on 38, the players warmly greeting the score 147-4.
Britain's goal was wounded by the shortfall of quick bowler Imprint Wood, who passed on the innings with an elbow injury and is presently an uncertainty for the subsequent Test, which starts on Wednesday in Barbados.
Prior, in spite of the deficiency of five wickets, Britain added 132 runs prior to announcing 20 minutes before lunch on 349-6.
Root transformed his 84 not out for the time being into 109, while Dan Lawrence scored 37 from 36 balls in a venturesome appearance as Britain looked for speedy runs.
The Test might have finished in a draw yet Britain's better execution on the last two days offers some force as they hope to continue on from their embarrassing 4-0 Cinders rout.
Response to day five in Antigua
Pitch impedes lively Britain
With the bowlers available to them, Britain did everything that could practically have been required from them as they continued looking for triumph on the last day.
Root proclaimed sooner than anticipated and slow left-armer Filter specifically bowled well, yet the sightseers were upset by a tame pitch.
After West Indies gradually arrived at 59-0, Ben Stirs up eliminated Brathwaite, getting him lbw with a ball that left low, yet there was little naughtiness in the pitch from there on.
Wood's additional speed was missed and, without it, seamers Chris Woakes and Craig Overton were insufficient.
Opener John Campbell was gotten at mid-on attempting to whack Filter over the top and Jermaine Blackwood was out lbw trudging across the line - two pitiful strokes that assisted Britain's with causing.
Be that as it may, when Bonner and Holder played themselves in they had the option to shield without any difficulty, even with defenders encompassing the bat.
Britain would have had a glint had they explored the lbw ruling against Holder however Root, vigilant after prior consuming two audits on hopeful lbw yells, was unaffected. The innovation showed Drain's conveyance would have hit leg stump.
Root hung on until there were just five balls left prior to tolerating the reason was lost.
Up-sides for Britain
Britain were forceful from the start and opener Zak Crawley, who continued on 117, was bowled attempting to strike a Holder yorker for 121.
That finished a stand of 201 among Crawley and Root, yet the Britain skipper proceeded to one of his most direct Test hundreds of years.
The chanceless thump saw him surpass Alastair Cook in the rundown of most Test tons as Britain skipper and will quiet any discussion around his re-visitation of number three in the batting request.
Maybe most amazing was Lawrence's concise innings which gave Britain force. Having been reviewed to the side for this Test, the 24-year-old broke the ball over the off-side from the start and hit one excessive six.
This series has been charged as another time for Britain after a run of one win in 14 Tests.
Lawrence's innings, in addition to the exhibitions of Drain, Crawley and first-innings centurion Jonny Bairstow are up-sides.
There is still a lot of worry about Woakes power abroad and Overton's wicket-taking danger at this level, while Stirs up, who has been nursing a side physical issue since the fourth Remains Test in January, bowled 41 overs in the match.
Britain should trust that doesn't return to hurt them.
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