Towhid Hridoy struck a composed 83 to anchor Bangladesh's innings of 274-5 after a nervous start against Australia in the final ODI match in Mirpur on Sunday.
Litton Das (58 off 78 balls) and Mosaddek Hossain (56 off 51) also contributed unbeaten half-centuries to give the hosts a competitive total in the dead rubber, with Bangladesh having already clinched the three-match series.
Bangladesh, missing regular captain Mehidy Hasan Miraz due to concussion, had a torrid start when Xavier Bartlett bowled opener Soumya Sarkar for two in the first over.
Tanzid Hasan and stand-in skipper Najmul Hossain Shanto steadied the innings with a 51-run second-wicket stand before Matt Renshaw struck twice in quick succession to leave Bangladesh reeling at 61-3.
Tanzid fell for 19, caught by Riley Meredith at mid-on after top-edging a sweep off Renshaw, who then trapped Shanto lbw for 24.
Hridoy held Bangladesh together through the middle overs with his 88-ball innings.
He shared a 92-run fourth-wicket partnership with Litton before the wicketkeeper-batter retired hurt with cramp on 48.
Hridoy went on to reach his 13th ODI half-century in an innings that included eight fours.
Litton returned to bring up his first ODI fifty at Mirpur, finishing with 58 off 78 balls and striking four fours and two sixes.
Mosaddek provided a late flourish and was unbeaten on 56 off 51 deliveries, including five fours and a six, his fourth ODI half-century in ODI cricket.
Bartlett and Renshaw picked up two wickets apiece for Australia.