But Hope shared an unbeaten 71 off 64 balls with Keemo Paul for the seventh wicket, in which Paul contributed only 18.
The West Indies needed 32 off the last 18 balls to win and scored 10, including a Hope six back over bowler Rubel Hossain.
The equation dropped to 22 off 12, and Hope brought victory in sight by hitting pacer Mustafizur Rahman for three boundaries — all of them from the same perfectly manufactured shot — in a 16-run penultimate over.
Paul ended up hitting the winning runs, as the West Indies finally beat Bangladesh on this tour after three heavy defeats in the tests and first one-dayer.
Hope’s match-defining innings of 146 not out off 144 balls was laced with a dozen boundaries and three sixes. It was his third century.
An ordinary start didn’t portend West Indies’ finish.
Chadrapaul Hemraj, who replaced Keiran Powell, was first out for 3.
Hope found support from Darren Bravo (27) and Marlon Samuels (26), who ensured the West Indies didn’t collapse as in the first ODI.
He and Bravo combined for 65 runs until Bravo was removed by fast bowler Hossain. Hope and Samuels shared 62 runs as they kept the asking run rate under control.
Once Mustafizur got Samuels caught by Mushfiqur Rahim, the Bangladesh bowlers took wickets at regular intervals.
But Hope remained unfazed. He brought up his third century with a single through cover point off 118 balls, and kept growing with confidence. Paul finally gave him much-needed support, and they held their nerve.
Their platform was set by the West Indies fast bowlers, whose controlled aggression at the end prevented Bangladesh from causing havoc.
Bangladesh scored just 26 runs in the last five overs as fast bowlers Kemar Roach and Oshane Thomas varied their pace cleverly to curb the batsmen’s aggression.
For Bangladesh, Shakib Al Hasan was the highest scorer with a 62-ball 65. Mushfiqur added 62 and opener Tamim Iqbal 50.
After being sent in to bat first, Bangladesh fell in trouble when opener Liton Das retired hurt because of an ankle injury, but he came back later to bat and made 8.
Imrul Kayes continued his horrible series, being dismissed for a duck before Tamim and Mushfiqur resisted.
They shared an 111-run stand but both of them were removed in three overs.
Just when West Indies appeared to take the control, Shakib and Mahmdullah (30) added 61 runs together to set up a late blitz.
But Thomas, with 3-54, and Roach, 1-39, left them at least 15 to 20 runs short which eventually turned out to be decisive.
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