West Indies vice-captain Ramnaresh Sarwan top-scored with 91 not out before their fast bowlers took command to defeat Bangladesh by 99 runs in a World Cup Super Eights match on Thursday.
The home team's first victory in the second round came too late after four defeats in a row had dashed their semi-final hopes and rendered the game inconsequential.
Sarwan steered West Indies to 230 for five before new-ball bowlers Daren Powell and Corey Collymore shared five of the first six wickets on a bouncy Kensington Oval pitch to reduce Bangladesh to 52 for six.
Bangladesh were eventually 131 all out in the 44th over to finish down the table with only one win in their first World Cup second-round appearance.
West Indies: Brian Lara (captain), Ramnaresh Sarwan, Chris Gayle, Shivnarine Chanderpaul, Marlon Samuels, Dwayne Bravo, Devon Smith, Denesh Ramdin, Daren Powell, Jerome Taylor, Corey Collymore.
Bangladesh: Habibul Bashar (captain), Javed Omar, Tamim Iqbal, Saqibul Hasan, Mohammad Ashraful, Aftab Ahmed, Mushfiqur Rahim, Mohammad Rafique, Abdur Razzak, Mashrafe Mortaza, Syed Rasel.