Shai Hope scored his second successive hundred of the series before Bangladesh restricted West Indies to 198-9 in the third and final one-day international in Sylhet on Friday.
Fresh from an unbeaten 146 off 144 balls in the previous match, Hope struck another unconquered knock of 108 off 131 to prop up the visitors in the series decider.
Off-spinner Mehidy Hasan led the attack for Bangladesh, finishing with career best figures of 4-29.
Skipper Mashrafe Mortaza and spinner Shakib Al Hasan claimed two wickets each after the hosts elected to bowl at the Sylhet International Cricket Stadium, hosting its first ever ODI.
Hope defied the spirited Bangladesh attack, hitting Shakib over the long off to bring up his fourth ODI century after the ninth wicket had fallen for 177 runs.
The opener, who signed off with 297 runs in the three-match series, also hit 10 fours in his fine innings.
The three-match series is locked 1-1 after Bangladesh won the opening match by five wickets on Sunday and West Indies bagged a four-wicket victory in the second match two days later.
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