James Anderson, needing three wickets to become the first England bowler to take 500 Test wickets, ended up wicket-less - his historic moment on hold, at least, until next week's third Test at Lord's.
Most remarkable of all was Hope, who hadn't hit a hundred in any of his previous 11 Tests.
Speaking after West Indies sealed their first Test win in England since 2000, Root told Sky Sports: 'They put us under pressure when we batted and then went past us when they got their opportunity to bat.
It was all the more impressive given that just over a week earlier they d suffered an innings and 209-run defeat inside three days in the first Test at Edgbaston.
England wrestled control of the second test away from the West Indies late on the fourth day on Monday, declaring its second innings on 490-8 and setting the tourists a tough target of 322 to win.
Hope, who scored 147 in the first innings, remained unbeaten on 118 in the second innings to take his side to a five-wicket win. It was about trying to get as many runs on the board as possible, so I'm actually pleased I got through the 90s a bit faster.
"We let them slip away and now we have to really fight hard to save this test match", Chase said. "For us, we have 317 runs to make tomorrow and we've still got to believe that we can win the game", he contended.
The opener pressed on to register his fifty off 98 balls with seven fours, Shai Hope reaching the same milestone in 28 few balls as England's frustration grew.
"[He's got] plenty of courage, plenty of character and plenty of determination - for a 24-year-old, that's a lot to have".
But Broad did reduce the West Indies from 46 for none to 53 for two.
Moeen Ali was operating from the Kirkstall Lane End.
England captain Joe Root, who bemoaned a day of dropped catches, described Hope's knock as "exceptional". The list of dropped chances was added to when Brathwaite offered a return catch to Broad which he couldn't hold, but the ball deflected into the non-striker's stumps with Hope well out of his ground.
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.
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.