Windies won Tuesday’s match in Dhaka by four wickets after losing the opener, levelling the three-match contest 1-1 and setting the stage for a series decider in Sylhet on Friday.
The Caribbean side last won an ODI series in 2014 at home against Bangladesh and are desperate to end the drought.
Since then, they have capitulated in 11 series, managing their best result with a draw against Afghanistan last year.
They came close to defeating Bangladesh in July on home soil, suffering a 2-1 loss. In October, they went down to India 3-1.
A win would remove some sting from West Indies’ humiliating drubbing by Bangladesh in the Test series in November and December, when the home side wrapped up both matches inside three days.
Opener Shai Hope hit a career-best 146 off 144 balls not out, as West Indies toppled Bangladesh’s 255-7 with two balls in hand to complete their first win in the tour.
Pace bowler Oshane Thomas worked up some lively pace to leave Bangladeshi batsmen unsettled in both the games.
This will be first ever ODI hosted in Sylhet, in Bangladesh’s northeast. The ground has hosted seven Twenty20 internationals and a Test.
The West Indies will wrap up their tour of Bangladesh with three Twenty20 Internationals.