Opener Hope hit an unbeaten 146 off 144 balls as Windies reached 256-6 in 49.4 overs after pace bowler Oshane Thomas claimed 3-54 to help the visitors restrict Bangladesh to 255-7 at the Sher-e-Bangla National Stadium.
Shakib Al Hasan top-scored with 65 off 62 deliveries for Bangladesh while Mushfiqur Rahim and Tamim Iqbal made 62 and 50 respectively after West Indies invited the hosts to bat first.
Bangladesh won the opening match of the series by five wickets on Sunday.
The third and final match will be held in Sylhet on Friday.
Brief Scores
Bangladesh 255/7 (50 Overs) : Shakib Al Hasan 65, Musfiqur Rahim 62, Tamim Iqbal 50, Oshane Thomas 3/54
Windies 256/6 (49.4 Overs) : Shai Hope 146*, Darren Bravo 27, Rubel Hossain 2/57, Mustafizur Rahman 2/63
