Brathwaite was on 34 with Samuels on 29 at the break, the pair having doubled the home side's total at that point after the early dismissals of Devon Smith and Darren Bravo.
Smith became James Anderson's 381st Test wicket, touching a delivery through to wicketkeeper Jos Buttler to depart for 11. In his 100th match at this level, the veteran seamer needs three more scalps to become the leading wicket-taker in Test history for England.
Pacer Kemar Roach led the improved effort for the home side with the ball at the start of the day, taking the wickets of Buttler and Broad to finish with the best innings figures of four for 94 as England, resuming at the overnight position of 341 for five, added only 58 more runs to be dismissed within 20 minutes of the lunch interval.
At one point, they lost four wickets for just four runs before Jordan and Anderson briefly frustrated the home side, necessitating the introduction of part-time spinner Samuels to end the innings with the wicket of Anderson.
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His departure was the trigger for the slide with Holder removing nightwatchman James Tredwell via Bravo's third catch of the innings at first slip.
Roach then joined in the rout as Buttler and Broad both failed to score, the usually attacking wicketkeeper-batsman being restrained for 21 deliveries before edging a delivery to his West Indies counterpart Ramdin while the fast bowler slashed a wide delivery unerringly to Jermaine Blackwood at backward-point.