The hosts were propelled to 338-7 in Basseterre by a 258-run partnership between Denesh Ramdin (169) and Darren Bravo (124), with the tourists never threatening the target as they finished on 247-8.
The stand was the third-highest by any nation in ODIs, and the Windies' total was their fifth-largest in their 50-over history.
Despite wicketkeeper Ramdin arriving at the crease with the hosts struggling at 12-2 in the fifth over, he and Bravo steered the Windies to a mammoth total.
Ramdin's 169 came off just 121 deliveries, and included eight fours and 11 sixes.
Bravo, meanwhile, took the comparatively modest 127 balls for his 124, that included seven fours and eight sixes.
The stand was eventually ended when off-spinner Mahmudullah (1-48) dismissed Bravo, while paceman Al-Amin Hossain (4-59) got rid of Ramdin and cleaned up late wickets after the West Indies had done the damage already.
The Bangladeshi chase got off to a horror start, as they were 2-2 inside two overs with each of Anamul Haque (0) and Imrul Kayes (one) back in the pavilion.
Opener Tamim Iqbal (55) put up a good fight, and added 99 for the third wicket with Mushfiqur Rahim (72).
Spinner Sunil Narine (1-31) nabbed Iqbal, before Rahim ended up falling to the Windies' best bowler Ravi Rampaul (4-29).
The West Indies won the series 3-0.
The two cricket nations will play in a one-off Twenty20 international on Wednesday, before a two-Test series starting September 5.