The tourists won the first of three ODI games by 52 runs, making 246 for nine before bowling out West Indies for 194.
Bangladesh skipper Shakib Al Hasan continued his good form with a half-century to build on Mohammad Ashraful's 57 as Bangladesh made a strong total.
West Indies then lost both openers cheaply in a poor start to their reply.
Al Hasan made the smart decision to open the bowling with spinner Abdur Razzak, who trapped Dale Richards leg before with his second delivery.
Andre Fletcher was bowled by seamer Syed Rasel, playing on, as the Caribbeans fell to eight for two.
Devon Smith struck a smart 65 and received some good support from Dave Bernard (38) but West Indies were never really in the running.
Razzak finished with figures of four for 39 to leave his team confident of completing a Test and one-day double series victory in Tuesday's second game.
SCORE BOARD
BANGLADESH
Iqbal c Fletcher b Roach 0
Siddique c Lewis b Bernard 36
Ashraful (run out) 57
Raqibul b Roach 12
Shakib c Dowlin b Roach 54
Rahim c Sammy b Lewis 11
Mahmudullah c Bernard b Miller 42
N Islam (not out) 7
Razzak lbw Roach 0
Rasel b Roach 7
R Hossain (not out) 1
Extras (B-1, LB-8, W-10) 19
Total (for 9 wkts, 50 overs) 246
Fall of wickets: 1-0, 2-74, 3-97, 4-128, 5-149, 6-228, 7-230, 8-231, 9-241.
Bowling: Roach 10-0-44-5, Pascal 4-0-29-0, Sammy 9-0-48-0, Bernard 10-1-31-1, Miller 9-0-50-1, Lewis 8-0-35-1.
WEST INDIES
Richards lbw Razzak 1
Fletcher b Rasel 5
Smith lbw Shakib 65
Reifer c Hasan b Mahmudullah 3
Dowlin b Razzak 10
Bernard c Iqbal b Islam 38
Sammy lbw Razzak 28
Lewis b R Hossain 21
Miller (not out) 16
Roach (run out) 0
Pascal lbw Razzak 0
Extras (B-4, LB-1, W-2) 7
Total (all out, 43.4 overs) 194
Fall of wickets: 1-2, 2-8, 3-23, 4-42, 5-120, 6-130, 7-171, 8-188, 9-191.
Bowling: Rasel 8-0-30-1, Razzak 9.4-0-39-4, Mahmudullah 7-0-38-1, Shakib 8-0-26-1, Islam 7-0-28-1, R Hossain 4-0-28-1.
