David Warner’s accomplished 166 were the bedrock for a 48-run win that took holders Australia top of the World Cup table and damaged Bangladesh’s chances of making the semi-finals.
Warner found some explosive form late on to push Australia to their second-highest World Cup score of 381-5.
Bangladesh chased gamely but could not kick on in the closing stages.
The four semi-finalists look set already – with 19 matches of the group stage still to play.
Australia look likely to be joined in the last four by hosts England, India and New Zealand, although fifth-placed Bangladesh will hope to take advantage of any slip-ups.
Warner now has scored two centuries in eight days – a fine return after serving a year-long ban for ball tampering – and becomes the first player in World Cup history to pass 150 twice.
Bangladesh, set a World Cup record target to chase, saw Mushfiqur Rahim bring up his 100 in the penultimate over as the two teams amassed the most runs in a men’s World Cup game.