After being sent in to bat, the visitors were well-placed at 106 for 2 thanks to fluent half-centuries from Alick Athanaze (52 off 33) and skipper Shai Hope (55 off 36).
However, a dramatic middle-order collapse saw them lose seven wickets for just 43 runs, leaving Bangladesh firmly in control at the innings break.
Bangladesh’s bowlers staged an excellent comeback, led by Mustafizur Rahman, who returned impressive figures of 3 for 21.
Spinners Nasum Ahmed (2/35) and Rishad Hossain (2/20) provided crucial breakthroughs in the middle overs, while Tanzim Hasan Sakib kept things tight early on.
Despite a late unbeaten 17 from Roston Chase, the West Indies failed to capitalise on their early momentum.
With a target of 150 runs, Bangladesh will back themselves to chase it down and level the three-match series after a disciplined bowling display under the lights in Chattogram.