David Warner smashed 166 - the highest individual score of the tournament so far in addition to a second personal three-figure score - as his side set their opponents 382 to win.
Despite a gutsy chase, marshalled by 102* from Mushfiqur Rahim, Bangladesh fell short - however the match did break the record for the most runs scored in a men's ICC Cricket World Cup match.
Aussie batters fire
Warner has drawn some criticism for his watchful methods so far in the competition, with the left-hander not scoring at the rate at which he has become renowned for despite notching nearly 300 runs prior to this game.
And despite eventually ending his knock with a strike rate of 112, it was only after he reached his century that he began to demonstrate a more expansive repertoire of shots.
Alongside his captain and fellow opener Aaron Finch (53), they put on 121 for the opening wicket before Finch gave Soumya Sarkar (3-58) his first wicket of the day.
If his first partnership was big, his second was massive.
Dovetailing with Usman Khawaja (89), the left-handed duo combined to add 189 together - however, there were questions asked regarding the sedate nature of the pair's intent.
Upon Warner's dismissal in the 45th over Glenn Maxwell strode to the crease, and the explosive all-rounder blasted a blistering 32 off only 10 balls to move his side from 300 to 350 in just 17 deliveries.
They looked set to post an even bigger total when Maxwell was in full flow having dispatched two boundaries and three sixes, but he was run out by Khawaja to prevent an enormous score being posted.
Spirited Tigers make a good fist of it
In the face of such an imposing target, Bangladesh must be given credit for the manner in which they set about chasing it down.
Despite Soumya being run out for 10, Tamim Iqbal (62) and Shakib Al Hasan (41) counter-attacked smartly.
Yet their hopes may have wavered when Shakib was caught at mid-on having mistimed a shot from a Marcus Stoinis (2-54) slower ball, with the all-rounder in pursuit of a third-successive hundred.
Mushfiqur played a smart innings, notching nine boundaries and a six in his 97-ball knock as he looked to shepherd his side over the line.
Alongside Mahmudullah (69 off 50), the pair looked to smash their way to an historic victory, but despite being ahead of the rate after 30 overs, they required over 14 an over with just ten overs left.
The latter eventually succumbed when trying to hit a fourth six over the leg-side boundary and was caught at deep mid-wicket, and as he departed so too did his side's last realistic hopes.