Keemo Paul picked up five wickets befroe Evin Lewis cracked 18-ball fifty to helps visitors 2-1 series win.
The all-rounder cracked a 26-ball 42* before claiming a fifer, as Bangladesh beat Windies by 36 runs in 2nd T20I.
Buoyant West Indies look to seal T20I series in the second game at Dhaka on Thursday.
Cottrell 4-28 kept Bangladesh to just 129, and Shai Hope then smashed a fifty off just 16 balls
Century from Shai Hope but in Vain as Bangladesh clinch series 2-1.
Both Saifuddin and Mithun played their last T20I against Sri Lanka in February before being laid low by injuries and poor form.
Also returning to the side are fast bowlers Williams and Sheldon Cottrell; Pollard, Russell miss out.
Shai Hope scored his third ODI century to seal a last-over thriller for West Indies to level the series 1-1 against Bangladesh in Dhaka.
Mushfiqur helps the chase after West Indies were kept to 195, with Mortaza and Mustafizur taking three wickets each.
Darren Bravo has been included in the Windies ODI squad for the upcoming three-match series against Bangladesh.
