Malinga then dismissed Saqib Al Hasan and Mohammad Rafique in the same over before Muralitharan sealed Bangladesh's fate by having Shahadat Hossain stumped.
After the hosts won the toss, Mohammad Ashraful (57) and Shakib Al Hasan (54) helped the Tigers score 246-9 in their 50 overs as Kemar Roach took 5-44.