Left-arm wrist spinner Lakshan Sandakan compounded the woes of the home side by dismissing opener Liton Das for 25 and Mosaddek Hossain for 10.
Liton cut a loose ball to Wanindu Hasaranga at backward point while Mosaddek, who was playing his first ODI in nearly two years, was caught by captain and wicketkeeper Kusal Perera.
Mushfiqur helped Bangladesh rebuild with Mahmudullah and the pair took the attack to the opposition.
Sandakan, who returned with figures of 3-54, broke the partnership as Perera took sharp a catch to dismiss Mahumdullah.
Mushfiqur, who made 84 in Sunday's 33-run win, brought up his hundred off 115 balls, glancing Chameera for four after rain halted the game twice. He was the last man dismissed.
Chameera finished with figures of 3-44 in 9.1 overs while fellow quick Udana claimed two wickets.