After limiting England to 258 all out in their first innings - Kemar Roach and Shannon Gabriel taking four wickets apiece - West Indies kept their noses in front for the most part and a decisive 144-run partnership between Hope and Kraigg Brathwaite on the final day followed their 246-run union in the first innings.
"We're test cricketers for a reason". If West Indies had been set a ridiculously high target they would have shut up shop for a draw.
He came into this match with a Test average of 18 and now he has become the first man ever to score two centuries in a match at this famous old ground.
Meanwhile West Indies captain Jason Holder insisted he d never lost faith in his players.
England lead this three-match series 1-0 after thrashing the West Indies by an innings and 209 runs in the first Test at Edgbaston.
There seemed little danger of a Windies win when Joe Root declared his side's second innings on 490 for 8 late on Monday'sfourth day.
England, in common with the West Indies, dropped catches and normally reliable first slip Alastair Cook floored Brathwaite, yet to add to his overnight four, off Stuart Broad. Hope was the more fluent and stylish, his half-century coming off just 70 deliveries compared to the 98 balls it took Brathwaite, but both played straight, the recipe for success on a pitch with uneven bounce, and took advantage of scoring opportunities when they presented themselves. "It takes a lot of character to come out after the beating we got".
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She said it was the third such occasion when the Khattar Government has badly let down the people. On the other hand, Ram Rahim, who was arrested a day ago, has been kept in Rohtak jail.
But Broad did reduce the West Indies from 46 for none to 53 for two.
The former eventually departed just before tea having helped the visitors to 197 without further loss, edging Moeen to Stokes at first slip as he fell five runs short of the slice of history that would shortly be claimed by Shai Hope.
Yet when Moeen Ali tempted Brathwaite into a drive just before tea to have him caught at first slip by Ben Stokes for 95, it left this most excellent of contests on an even sharper knife edge.
A mixture of calm defiance combined with judicious attacking saw them frustrate the England attack to the point that James Anderson, who had a run-in with opener Kieran Powell, and Stuart Broad, who was warned for kicking the pitch petuantly, were left increasingly disgruntled.
Jermaine Blackwood was positive as he slashed his way to 41 off 45 balls to send the home team's fielders scurrying all over Headingley before he was out stumped with two runs still needed.
When Hope did offer a chance, slashing at Broad on 106, Cook could not hold on to the rapid chance and the batsman rubbed salt in the wound by upper-cutting the seamer for six.