Having ended a 21-year wait for an ODI victory over Australia in the series opener, the Tigers went one step further in Mirpur, taking an unassailable 2-0 lead in the three-match series against the six-time World Cup champions.
The hosts laid the foundation for victory with a devastating new-ball spell that left Australia reeling at 0 for 3.
Taskin Ahmed and Mustafizur Rahman ripped through the top order, dismissing Matthew Short, Cooper Connolly and Matt Renshaw without a run on the board, handing Australia an unwanted ODI record.
Despite the collapse, Marnus Labuschagne fought back with an unbeaten 55, while Xavier Bartlett struck a counter-attacking 52.
Their 103-run partnership rescued Australia from complete disaster and helped them reach 187 for 8 in a rain-shortened 42-over innings.
Taskin and Mustafizur finished with three wickets apiece, while Tanvir Islam claimed two crucial scalps.
After further rain delays, Bangladesh were set a revised target of 192 from 41 overs under the DLS method.
The chase began poorly as Tanzid Hasan fell for a duck, but Soumya Sarkar and Najmul Hossain Shanto steadied the innings with identical knocks of 42. Litton Das added a brisk 21 before Towhid Hridoy and captain Mehidy Hasan Miraz guided the hosts home.
Hridoy remained unbeaten on 40, while Miraz struck an unbeaten 22 as Bangladesh reached 195 for 5 in 35 overs, sealing victory with six overs to spare.
The triumph marks Bangladesh's first bilateral ODI series win over Australia in men's cricket.
Before this series, their only ODI victory against the Australians had come in the famous 2005 Cardiff upset, making this achievement another significant milestone for the Tigers.
With the series already secured, Bangladesh will now aim for a historic clean sweep when the two sides meet in the final ODI in Mirpur.
