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Matthew Wade, a stand-in captain, scored 22 points for Australia
Fifth Twenty20, Mirpur Bangladesh: 122-8 (20 runs): Naim 23, (23) Australia: 62 all out (13.4 runs): Wade 22, (22); Shakib 4,-9 Bangladesh won by 60 runs Scorecard
Australia lost to Bangladesh by a run and were bowled out for just 62 runs.
The tourists were out in 13.4 innings, their shortest innings in 144-years. Only Matthew Wade and Ben McDermott passed four.
Bangladesh's Shakib al Hasan claimed 4-9 and became the first player in history to score 1,000 T20 runs.
Before this series, the Tigers had never defeated Australia in T20 before.
Bangladesh scored 122-8 in 20 overs. Mohammad Naim, the opener, scored 23.
Australia managed only three sixes and no fours in its woeful chase.
They were without Aaron Finch, their captain, and fellow batters Steve Smith, Glenn Maxwell and David Warner for the series.
The T20 World Cup in Oman and the United Arab Emirates is set to begin on 17 October.