The last time the Tigers victorious in a 50-over contest against the Aussies came in June 2005 in Cardiff, with the result a massive upset at the time.
This result though was not an upset as Bangladesh continued their impressive form in the format after recently beating Pakistan in a home series.
After being put in to bat at the toss, Mosaddek Hossain struck an unbeaten 86 from 70 balls as Bangladesh got to a total of 284-8 in their 50 overs.
A good platform was laid at the order with opener Tanzid Hasan hitting 54 and number 3 Najmul Hossain Shanto scoring a patient 67 in a 96-run partnership for the second-wicket.
Nathan Ellis was the pick of the Australia bowlers with figures of 3-38 in his 10 overs while debutant seamer Liam Scott and spinner Matt Renshaw both picked up two scalps.
The Australia run-chase got off to the worst possible start when Matthew Short and Marnus Labuschagne were dismissed with only two runs on the board.
Alex Carey scored 47 while Cameron Green was unbeaten on 52 but fast bowler Nahid Rana was relentless with his pace and took 4-41 in 10 overs.
The visitors were 191-9 in the 43rd over when a thunderstorm stopped pay and the players never never returned to give Bangladesh a famous victory.
Mitchell Marsh has been ruled out of Australia's ODI series in Bangladesh with an ankle injury while Travis Head will the tour to manage his workload following a gruelling IPL season.
Former Australia fast bowler Shaun Tait has stepped down from his role as Bangladesh pace bowling coach with immediate effect, bringing an abrupt end to a one-year spell in charge.
Mosaddek Hossain has been recalled into the Bangladesh ODI squad after a four-year absence for the upcoming home series against Australia that starts next week.
Nathan Ellis took four wickets as Australia defended a target 232 to beat Pakistan by 41 runs in the second ODI in Lahore as the visitors levelled the three-match series with one game left to play.
