Bangladesh's last seven wickets fell for 13 runs and the only man to reach double figures for the tourists in a miserable batting display was Tamim Iqbal who made 37.
West Indies made a creditable 247 for seven with opener Chris Gayle striking five sixes in his 58 off 67 balls.
Gayle was well supported by Darren Bravo (53) but skipper Denesh Ramdin (34) and Lendl Simmons (40) were unable to keep up the run-rate, leaving Bangladesh needing just under five an over.
Although West Indies will be pleased with their bowling they were helped by some poor strokes from Bangladesh, particularly from their middle order.
Jason Holder had opener Anamul Haque caught behind by Ramdin for seven and Imrul Kayes holed out to Simmons at deep mid-wicket off Ravi Rampaul.
Shamsur Rahman played on to Roach, still working his way back to his full pace after shoulder surgery, but it was the clever spin of Narine that did the bulk of the damage.
Narine removed Mushfigur Rahim and Mahmudullah in successive balls to reduce Bangladesh to 57 for five and the tourists never looked like recovering as their tail surrendered.
(Reporting by Simon Evans, editing by Ed Osmond)
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