Spinners Ashan Priyanjan (2-11) and Ajantha Mendis (2-55) put the brakes on after Bangladesh won the toss and made a promising start, before Thisara Perera (2-29) and Suranga Lakmal (2-32) wrapped up the middle and lower order.
Opener Anamul Haque, who scored a brilliant hundred in Bangladesh's highest one-day score of 326-3 against Pakistan on Tuesday, was once again the mainstay of the batting with a 86-ball 49.
Anamul and Shamsur Rahman (39) gave the home team a solid 74-run start before Mendis struck twice, dismissing Shamsur and Mominul Haque (one) in the 18th over.
Anamul hit two boundaries and a six during his 86-ball knock while Shamsur's 57-ball innings included six hits to the fence.
Nasir Hossain (30) and Mohammad Mahmudullah (30) shared an innings-repairing sixth wicket stand of 55 to give the total some respectability.
Shakib Al Hasan made 20.
The match will not affect the competition because Sri Lanka and Pakistan have already qualified for Saturday's final.
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