Bangladesh have lost their seventh wicket as Mehidy Hasan Miraz was dismissed by Mitchell Starc.
On tenterhooks, Tigers lost two quick wickets soon after crossing 300-run mark chasing the mammoth target of 382 to beat Australia.
The Aussies were kept warried on the partnership by Mushfiqur Rahim and Md Mahmudullah, until Nathan Coulter-Nile took out the latter before dismissing Shabbir Rahman scoring a two in two.
Tigers lost their fourth wicket as Liton Das was plumb lbw following his 20 runs off 17 balls.
Opener Tamim Iqbal was bowled out by Mitchell Starc after scoring 62 runs off 74 balls taking the Tigers to three down.
Bangladesh lost their second wicket as Marcus Stoinis claimed Shakib Al Hasan’s wicket.
A slower ball from right-arm medium bowler saw Shakib caught out at mid off after scoring 41 runs from as many balls.
Tigers' loss of first wicket was with Soumya Sarkar run out by Aaron Finch.
Bangladesh started its chase for a mammoth target of 382 decently but a mixup from the openers saw Soumya falling to a run out.
Earlier the Aussies racked by 381-5 powered by in-form opener David Warner's 166, the highest score of the 2019 Cricket World Cup.
Warner, whose second century took his tournament-leading tally to 447 and captain Aaron Finch, with 396 to his name, yet again laid the platform with a carefully-constructed opening stand of 121.
Usman Khawaja added 89, though not at a speed Australian fans would have wanted, before Glenn Maxwell picked up the pace by smashing 32 from 14 balls before being run out.
Steve Smith was then plumb lbw for one - after a contender for the worst review of the tournament. Marcus Stoinis (not out 17) and Alex Carey (not out 11) took over and, after a rain interruption forced them to briefly go off with an over to go, finished with something of a flurry.
Soumya Sarkar was the best of the Bangladesh bowlers, taking three for 58 in eight overs on a batsman-friendly track.
Having chased down 322 with eight overs to spare against the West Indies on Monday, Bangladesh will still have some hope of claiming the victory they almost certainly need to maintain their hopes of breaking in to the top four but it would need the second-highest run chase in one day cricket to achieve it.
Only South Africa's incredible 438 to beat Australia in 2006 would top it, while the highest previous successful chase in a World Cup was Ireland's 329 against England in 2011.
"You've got to be confident with 380 on the board but you've got to come out and bowl well in the first 10 overs and look to take wickets, bowl some dots and build up some pressure," said Warner.