Openers Alyssa Healy and Phoebe Litchfield made light work of a 199-run chase, sealing victory in just 24.3 overs.
The result took Australia to the top of the group standings with nine points from five matches, while defending champions Bangladesh remained in sixth place with only two points.
Healy led from the front with a blistering unbeaten 113 from just 77 balls, smashing 20 boundaries in a dominant display that marked her second century of the tournament. Litchfield was equally composed at the other end, finishing 84 not out with 12 fours and a six. The pair's unbroken 199-run opening stand was one of the most commanding partnerships of the competition.
Earlier, Sobhana Mostary's resilient knock had helped Bangladesh post a respectable 198 for 9 after being put in to bat. Mostary remained unbeaten on 66 off 80 balls, striking nine fours and accelerating late in the innings with 28 runs coming off the final three overs. Rubya Haider added a valuable 44, but regular wickets prevented Bangladesh from building momentum.
Australia's bowlers were once again on target, with leg-spinners Alana King (2 for 18) and Georgia Wareham (2 for 22) proving particularly effective. Ashleigh Gardner (2 for 45) and Annabel Sutherland (2 for 42) also shared wickets despite being slightly expensive, while Megan Schutt picked up the first breakthrough to remove Farzana Haque.
Bangladesh slipped from 67 for 1 to 165 for 9 before Mostary's late hitting ensured they were not bowled out, the first time Australia failed to dismiss a side completely in this tournament.
But any hopes of an upset quickly vanished as Healy and Litchfield dominated from the outset, guiding the six-time champions to a flawless victory and yet another semi-final berth in their illustrious World Cup history.
Australia's women's captain, and one of the most successful players in the sport, Alyssa Healy has confirmed plans to retire from all forms of cricket after the home series against India.
The ICC has said there is no specific or heightened security threat for Bangladesh playing in India at the T20 World Cup, even though the country's sports adviser said they still have concerns.
Bangladesh batter Najmul Hossain Shanto admits "it is not easy" to perform in global tournaments when off-field controversies continue to haunt the team.
The Bangladesh Cricket Board (BCB) says the ICC "has conveyed its willingness to work closely" with the country due to security concerns about playing in India at the T20 World Cup.
