Towhid Hridoy's maiden World Cup fifty took Bangladesh to 306-8 against Australia in Pune on Saturday.
The 22-year-old's 74, his sixth fifty in 24 one-day internationals, was the cornerstone of Bangladesh's highest total of the tournament.
Adam Zampa was the pick of Australia's attack with 2-32 as the leg-spinner became the outright leading bowler in the tournament with 22 wickets, while Marnus Labuschagne ran out the well-set Najmul Hossain Shanto (45) and Mahmudullah (32).
Australia now needed to surpass their record World Cup winning chase of 292 against Afghanistan in Mumbai on Tuesday.
But they were without double-century hero Glenn Maxwell, the all-rounder rested after his breathtaking 201 not out revived Australia from the depths of 91-7 to seal a three-wicket win in that game.
Although this was a 'dead' game, with Australia already assured of a semi-final against South Africa next week and Bangladesh unable to reach the knockout stages, there was still something riding on it for both teams.
Five-time champions Australia wanted to maintain the momentum that had seen them win six matches in a row after losing their first two games.
Bangladesh, who'd lost six of their eight games, were looking for a victory in a quest for a top-eight finish that would qualify them for the 2025 Champions Trophy in Pakistan.
Tanzid Hasan and Liton Das put on 76 after Australia captain Pat Cummins won the toss but both openers fell for 36.
Sean Abbott, in for rested fellow fast bowler Mitchell Starc, produced a fine short ball to have Tanzid caught and bowled on his World Cup debut.
Left-hander Najmul, leading Bangladesh in place of captain Shakib Al Hasan, out with a broken finger, hit six fours, before he was needlessly run out by Labuschagne's excellent throw to wicketkeeper Josh Inglis to end a stand of 64.
Mahmudullah, the only Bangladesh batsman to have scored a hundred at the tournament, hit three sixes before the 37-year-old veteran was run out for 32 by a superb under-arm throw from the diving Labuschagne.
Hridoy had just completed a 61-ball fifty when he was dropped by Inglis who just failed to hold a spectacular one-handed catch off a top edge as he ran back.
He was eventually dismissed when he holed out off Marcus Stoinis to spark a flurry of wickets as the innings fell away.
Brief scores: Bangladesh 306-8 in 50 overs (Towhid Hridoy 74) v Australia
