|Hussey steadied the ship before Bangladesh threw the game away [AFP]
Michael Hussey struck a sparkling 47 not out and Dirk Nannes took four wickets to help Australia beat Bangladesh by 27 runs and qualify for the Super Eight stage of the World Twenty20 in Barbados.
The one-day world champions were struggling at 65 for six after fine bowling and fielding from Bangladesh with two wickets apiece for Mashrafe Mortaza and Shakib Al Hasan.
Bangladesh, who have lost their last 12 matches in the shortest format of the game, sensed the chance to end that run with what would have been the first major upset of the tournament.
Instead they are eliminated and were left to rue the way they allowed Australia to claw back to a decent total and then surrendered with some poor top-order batting.
"I thought we had a very good chance. We should have chased 140 runs," said Tigers' skipper Al Hasan on Wednesday.
"We did not bowl very well in the last four overs, and we played too many shots early in our innings. We need to take the big step forward in these games and start winning some of them."
Bangladesh's excited celebrations of their wickets, cheered by an afternoon Kensington Oval crowd made up largely of schoolchildren, revealed a team that despite that three-year losing streak, truly believed they could beat Michael Clarke's side.
But Hussey and Steven Smith added a vital 74 runs in seven overs to lift the Aussies to 141 for seven.
Hussey bats down at seven in Twenty20 precisely to act as an insurance policy if the big hitters at the top of the order fail.
That can be a thankless task at times with the classy Hussey usually forced to slog in the final few overs but on Wednesday, Australia needed to call on his intelligent and accomplished strokeplay.
"I was just trying to get a partnership going, before the slog in the end overs. Smithy played a good innings and we got up to 140. Thankfully today was my day -- you have plenty of bad days batting lower down, so you got to enjoy the good ones," he said.
Bangladesh knew they had to win with a swift run-rate to qualify for the next stage ahead of Pakistan but they were never really in the running after slumping to 15 for four.
As so often, the impressive Al Hasan provided resistance with a spirited 28 from as many balls before he was caught superbly by Hussey at full stretch on the boundary.
Hussey also caught Mushfiqur Rahim, who had batted with character, off the bowling of his brother David and Bangladesh were bowled out for 114.