Shane Watson smashed Bangladesh into submission with 185 not out as Australia opened an unassailable 2-0 lead in the one-day series.
Watson's contribution, the highest by an Australian in the 50-over format, took only 96 balls and featured 15 fours and 15 sixes - a record number of maximums in an ODI innings.
Chasing a target of 230 in Mirpur, the visitors cruised home for a nine-wicket victory with a full 24 overs to spare.
Brad Haddin was the only wicket to fall during the run chase, caught by Mahmudullah off Shakib Al Hasan's bowling in the ninth over after contributing eight to an opening stand of 62.
Thereafter it was the Watson show as the powerful Queenslander took a liking to all of the Bangladesh bowlers - he needed only 26 balls to bring up his half-century and advanced to his sixth ODI hundred from 69 deliveries.
Watson was given a life immediately after bringing up three figures, Abdur Razzak failing to hold on at long-on off Shafiul Islam's bowling (0-27).
Spinner Razzak (0-58) almost made amends but Raqibul Hasan grassed a tougher chance on the midwicket boundary - and in the next over, bowled by young left-arm spinner Suhrawadi Shuvo (0-46), Watson dispatched four sixes in a row.
The 29-year-old, promoted to the vice-captaincy for this tour, hit three more sixes to his favoured midwicket region off Razzak in the 25th over.
Watson's final six, this time lofting a Rubel Hossian (0-57) delivery straight back over his head, took him beyond Matthew Hayden's 181 against New Zealand in February 2007 as the highest ODI score for Australia.
Former skipper Ricky Ponting, who was responsible for 37 of a second-wicket partnership worth 170, hit the winning runs two balls later.
The Tigers had earlier posted a score of 229-7 after opting to bat first at the Shere Bangla National Stadium.
Left-arm paceman Mitchell Johnson (3-54) struck twice with the new ball to put them in early trouble at 28-3.
Shahriar Nafees averted total meltdown with 56 but his dismissal, caught-and-bowled by leg-spinner Steve Smith (2-34), left Bangladesh on 88-5 in the 27th over.
Mushfiqur Rahim rallied the lower order with 81 not out from 80 balls and received solid support from Mahmudullah (38) in a sixth-wicket alliance of 79 - although Watson's brutal display then put a flat pitch into stark perspective.
The three-match series concludes at the same venue on Wednesday.