The West Indies had Jason Holder to thank as the all-rounder conceded only four runs in the final over to draw the ODI series level with Bangladesh.
The tourists went into the last over of the day-night match needing only seven to win, but Holder took the vital wicket of Mushfiqur Rahim (68) with the first ball, the batter holing out at deep midwicket.
Only four runs were scored from the remaining five balls as the Windies took the three-run win in Providence.
Shimron Hetmyer's 93-ball 125 helped the West Indies to set a target of 272, while Rovman Powell's steady 44 from 67 also helped keep the scoreboard ticking over.
Holder had gone for nearly seven an over before saving his side at the death.
He removed the Bangladesh top scorer and restricted Mosaddek Hossain and Mashrafe Mortaza as the best-of-three series was levelled up 1-1.
