The match was reduced to 40-overs a side after overnight rain delayed the scheduled start by two hours and 15 minutes.
Sri Lanka made three changes to the side that won the second one-dayer on Monday to clinch the series 2-0, resting Lasith Malinga, Chamara Silva and Malinga Bandara.
The trio was replaced by Chamara Kapugedera, Upul Chandana and Nuwan Kulasekara.
Bangladesh dropped Shahriar Nafees and Tushar Imran to bring in Javed Omar and uncapped Mohammad Mahmudullah.
Sri Lanka: Mahela Jayawardene (capt), Sanath Jayasuriya, Upul Tharanga, Kumar Sangakkara, Nuwan Kulasekara, Tillakratne Dilshan, Jehan Mubarak, Farveez Maharoof, Upul Chandana, Chamara Kapugedera, Dilhara Fernando.
Bangladesh: Mohammad Ashraful (capt), Tamim Iqbal, Javed Omar, Mohammad Mahmudullah, Shakib Al Hasan, Aftab Ahmed, Mushfiqur Rahim, Farhad Reza, Shahadat Hossain, Abdur Razzak, Syed Rasel.
Umpires: Asoka de Silva (SRI) and Rudi Koertzen (RSA), TV umpire: Ranmor Martinez (SRI)
Match referee: Jeff Crowe (NZ)