New-ball partner Suranga Lakmal finished with two for 24 in 10 overs after Sri Lanka, enjoying an unassailable 2-0 lead in the series, won the toss and elected to field at the Sher-e-Bangla stadium.
Mominul Haque top-scored with a run-a-ball 60, while valuable contributions from Nasir Hossain (38), Naeem Islam (32) and skipper Mushfiqur Rahim (30) gave the hosts their highest score in the series.
Sri Lanka took the field without either of their three veterans, Mahela Jayawardene, Kumar Sangakkara and Tillakaratne Dilshan, for the first time in a one-dayer since 2000.
The hosts missed premier all-rounder Shakib Al Hasan, who was handed a three-match ban for a lewd on-camera gesture during the second one-dayer on Thursday.
Sri Lanka won both the preceding Test and Twenty20 series.
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