After crashing to an unprecedented 3-0 from the first two overs at Sher-e-Bangla National Stadium in Dhaka on Tuesday, the Aussies recovered to salvage 8-187 from 42 overs when rain forced the players off the field at Mirpur.
Play was delayed for 160 minutes before Bangladesh, set a revised target of 192 from 41 overs via DLS method, strolled to victory - and an unassailable 2-0 series lead - with 36 balls in hand, sealed by captain Mehidy Hasan Miraz's six off Riley Meredith.
Australia were behind the eight-ball from the outset, creating unwanted history by losing their first three wickets before scoring a run for the first time in ODIs.
Under-pressure Marnus Labuschagne (55 not out) and tail-ender Xavier Bartlett (career-best 52) helped avoid complete embarrassment for the tourists, who, after winning the toss and electing to bat, lost top-order trio Matt Short, Cooper Connolly and Matt Renshaw for ducks.
Short was castled shouldering arms to Taskin Ahmed, his tormenter in the first game, for his third straight zero dating back to the recent Pakistan series.
Connolly and Renshaw both nicked Mustafizur Rahman to wicketkeeper Litton Das in the second over.
Stand-in Australian captain Josh Inglis said: "Any time you lose three wickets that early, it's tough to come back from. Marnus and 'X' (Bartlett) got us to total, but it wasn't enough.
"Bangladesh have outplayed us in this series, so congratulations to them."
It was 4-25 when Alex Carey (13) departed, before Josh Inglis (34) and Cameron Green (25) both fell to Tanvir Islam's spin, the tourists reeling at 6-81.
Labuschagne, demoted to No.7, snapped a protracted form drought by posting his first half-century in his past 18 ODIs, combining with unlikely batting hero Bartlett for a 103-run seventh-wicket stand to give Australia an outside chance.
Taskin ended the union when he bowled Bartlett and the Tigers seamer was on a hat-trick when he skittled Adam Zampa next ball, soon before the heavens opened.
Bangladesh's reply started badly when Tanzid Hasan (0) spooned the second delivery of the innings back to Xavier Bartlett for a return catch.
Bartlett spilled a tough chance from Najmul Hossain Shanto three balls later before having a successful lbw shout overturned on DRS in an eventful first over.
Soumya Sarkar (42) and Najmul (42) steadied the ship with an 86-run second-wicket stand, before Towhid Hridoy (44no) and Mehidy (22no) finished the Aussies off.
Bangladesh, who hadn't beaten Australia since 2005 before the series, have now overcome them twice in 48 hours.
The Tigers have won four straight bilateral ODI series after also defeating New Zealand, Pakistan and West Indies.
The third and final game will be in Dhaka on Sunday
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