ICC World Twenty20, Barbados:
Australia 141-7 (20 overs) beat Bangladesh 114 (18.4 overs) by 27 runs
Tait claimed a wicket in his first over to set Australia on the road to victory
Australia overcame a shaky start to beat Bangladesh by 27 runs and reach the ICC World Twenty20 Super Eights.
The Tigers looked on course for a shock victory when they reduced the Aussies to 65-6 in the 13th over.
But a superb unbeaten 47 from Mike Hussey and a handy 27 from Steven Smith hauled Australia to a decent 141-7.
Shaun Tait and Dirk Nannes (4-18) ripped through the Bangladesh top order as the Tigers were skittled for 114 to go out of the competition.
Australia's victory ensured defending champions Pakistan also progressed from Group A, and Shahid Afridi's men will take on England in the first Super Eight contest on Thursday.
The Australians, winners of the last three 50-over World Cups, have struggled to impose themselves in the game's shortest form.
After reaching the semi-finals of the inaugural ICC World Twenty20 in 2007 they were knocked out at the first hurdle in England last year.
The Tigers have not matched their Test progress in the Twenty20 arena, and have now lost their last 12 internationals.
Bangladesh made a bright start with Mashrafe Mortaza enjoying the extra bounce in the Barbados pitch and troubling openers David Warner and Shane Watson.
The paceman struck in his second over as Watson top-edged a pull shot and was caught by Aftab Ahmed in the deep.
Warner, who had shown his power with a straight six and four in successive balls off Mortaza, went for another big shot off the spin of Shakib Al Hasan but his leg-side heave presented Aftab with a straightforward catch.
With Shakib operating in tandem with fellow left-arm spinner Abdur Razzak, Bangladesh maintained their stranglehold on the game and struck again when Brad Haddin sliced a catch to Shafiul Islam.
Captain Michael Clarke did his best to steady the ship in the face of some tight spin bowling but, after accumulating 16 from 21 balls, he also succumbed to frustration as his lofted drive picked out Jahurul Islam at long-off.
David Hussey, dropped by Jahurul off his first ball, was the next to fall as a dismal shot flew into the air and was snaffled by wicketkeeper Mushfiqur Rahim, before Shakib bowled Cameron White for eight.
More than 10 overs passed without a boundary before Mike Hussey pulled a short ball to the square-leg rope and dispatched two leg stump full tosses for a six and a four.
Hussey's fluency seemed to inspire Smith, who smashed two sixes in the penultimate over to lift his side to a respectable total.
Australia needed a good start with the ball and Tait obliged, rattling Imrul Kayes with some fearsome deliveries before surprising him with a slower ball which the batsman lofted straight to mid-off.
Nannes, who played for the Netherlands in the 2009 tournament, continued the onslaught with three quick wickets to reduce the Tigers to 15-4.
A breezy partnership of 48 between Shakib and Mushfiqur Rahim threatened to bring Bangladesh back into the match but Shakib went for one big shot too many and was brilliantly caught on the boundary by a diving Mike Hussey.
Spinners David Hussey and Smith claimed two wickets apiece and after Nannes had claimed his fourth wicket of the match, Ryan Harris wrapped up the victory with a full straight delivery which flattened Mortaza's stumps.