Bangladesh were lifted to 153-5 by Shakib Al Hasan's 66 and 47 by skipper Mushfiqur Rahim.
Australia smashed the target in 17.3 overs for the loss of three wickets. Aaron Finch made 71 and David Warner scored 48.
Hosts Bangladesh, who qualified from the first round, finished the Super-10 stage with four defeats in as many games.
India, South Africa and Sri Lanka have qualified for the semi-finals. The fourth and final pre-final spot will be decided after a Pakistan-West Indies match in Dhaka later Tuesday.