Mashrafe Mortaza led Bangladesh's fightback in the field before Tamim Iqbal, Soumya Sarkar and Shakib Al Hasan struck fifties to power their side to a convincing eight-wicket win over the West Indies in the second match of the tri-series in Dublin.
Shai Hope (109) hit his second ton of the series in as many games. West Indies were well-placed at 205-2 in the 41st over before a collapse restricted them to 261-9 in 50 overs, with skipper Mortaza taking 3-49.
Tamim then made 80 and shared an opening stand of 144 with Soumya Sarkar (73).
Shakib Al Hasan followed up with 61* with Bangladesh winning with five overs to spare.
Tamim was dropped on one by Roston Chase.
Earlier, Hope carried on from his excellent form against Ireland in the triangular series opener where he made 170 in a commanding victory. But despite adding 115 runs for the third wicket, Hope and Chase (51) were restricted by Shakib and Mehidy Hasan Miraz, who between them had combined figures of two for 71 from 20 overs.
The series continues on Thursday when Ireland play Bangladesh.