The pair shared a 246-run partnership as West Indies, written off after a humiliating innings-and-209-runs defeat in the first test, reached stumps on 329-5, a lead of 71.
Brathwaite was eventually bowled by Stuart Broad for 134, a textbook innings which contained 17 fours and two sixes, the second of which took him to his sixth test century.
Roston Chase followed shortly afterwards but Hope moved on to 147 and was joined by Jermaine Blackwood who played aggressively to score 21 not out in 23 balls.
West Indies resumed on a muggy morning on 19-1, and with James Anderson swinging the ball at will, another West Indies collapse looked on the cards as two early wickets fell.
Nightwatchman Devendra Bishoo departed in the fifth over of the morning, edging one from Anderson who then removed Kyle Hope thanks to a great catch from captain Joe Root at second slip.
Brathwaite was then joined by Hope and the duo began to chip away at England's total, playing with discipline and verve to put away any loose balls from England's attack.
Twice Braithwaite was reprieved with successful reviews after being given out lbw -- to Broad when he got an inside edge and to the struggling Moeen Ali -- as West Indies moved to 109 for three at lunch.
The afternoon session belonged to West Indies as Brathwaite completed his century by launching part-time spinner Tom Westley over long-on for a huge six.
Hope offered impressive support and played some beautiful cover drives as he also closed in on a century, reaching 85 at tea as England's bowlers desperately sought a breakthrough.
His maiden test century arrived in the 70th over of the day when, after pulling Ben Stokes for a boundary, he nudged a single off his hip from the following ball.
With Hope set and Blackwood a dangerous hitter, West Indies will hope to build a commanding lead on Sunday.
(Reporting by Martyn Herman; Editing by Clare Fallon, Neville Dalton)
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