Replying to the home side's total of 247 for seven in a match they had to win to keep the series alive following a three-wicket defeat in the opening fixture at the same venue two days earlier, the tourists showed little resistance in being routed for 70 off 24.4 overs yesterday.
The third and final match will be played next Monday in St Kitts.
In capitulating to their third lowest ODI total, Bangladesh lost their last seven wickets for 13 runs in the space of eight overs.
His was the last of three wickets to fall with the score on 57, popping up a simple catch to midwicket off Roach after Narine had effectively ended any chance the tourists had of an upset set win when he removed Bangladesh captain Mushfiqur Rahim and Mahmudullah off successive deliveries in the 16th over.
Narine snared three for 13 to take the man of the match award while Roach played his part with figures of three for 19.
Half-centuries by Chris Gayle and Darren Bravo anchored a solid if unspectacular West Indies batting effort after they took first strike in overcast, bowler-friendly conditions.
Gayle's 58 at the top of the order, which included five sixes and three fours, together with Bravo's comparatively serene 53 ensured there was to be no repetition of the embarrassing collapse in the first ODI when the West Indies crashed to 34 for five before Kieron Pollard and Denesh Ramdin successfully resurrected the effort in pursuit of a target of 218.
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