Pat Cummins (3-29) became only the fourth Australian to record a T20I hat-trick, joining forces with the in-form Adam Zampa (2-24) to restrict Bangladesh to 8-140 with the bat on Friday (AEST).
Two separate rain delays interrupted Australia's run chase, but the retiring David Warner (53 not out from 35 balls) ensured they were well ahead of the DLS par score when play was called off in the 12th over.
Mitch Marsh's side finished at 2-100.
The win means Australia are likely to progress to the final four at the North American tournament if they beat Afghanistan in their second of three Super Eight games on Sunday.
"We're playing well, but there's still a long way to go," Marsh said.
With AAP.
