Perera scored a 122-ball 120 while Chameera picked up his best ODI figures of 5 for 16.
Bangladesh, with this win, atop World Cup Super League points table.
Mehidy Hasan picks four, Bangladesh overcome Hasaranga (74) fightback to win first ODI.
Bangladesh announced a 15-member squad for the first two ODIs of the home series against Sri Lanka, starting 23 May.
Kusal Perera to captain Sri Lanka in any format in International Cricket for the very first time.
Bangladesh and Sri Lanka eye chance to climb Super League standings.
