After winning the toss, the Tigers chose to bat and set a target of 321 runs after losing seven wickets in the third match of the tri-nation series.
Opener Tamim Iqbal struck 84 on way to reaching 11,000 international runs, while Shakib Al Hasan scored 67 to get to the 10,000-run milestone. Mushfiqur Rahim scored 62 runs off 52 balls.
The Lankans were all out for 157 in the 33rd over.
Shakib took three wickets for 47 while skipper Mashrafe bin Mortaza and paceman Rubel Hossain got two wickets each. Nasir Hossain and Mustafizur Rahman chipped in with one wicket apiece.
