Australia have kept alive their hopes of qualifying for the knockout stages of the World Twenty20 in India by edging past Bangladesh in a tight game in Bangalore.

Steve Smith's side were beaten by New Zealand in their first match and a second straight defeat today would have almost certainly cost them a place in the last four.

However, a strong showing from Glenn Maxwell in the middle-order helped the Aussies over the line by three wickets against Bangladesh, whose own slim semi-final hopes appear to now be over.

Australia put Bangladesh in to bat after winning the toss and Shane Watson quickly removed Soumya Sarkar (1) in the second over.

Shakib Al Hasan (33) and Mahmudullah (49 not out) were Bangladesh's top scorers as they posted 156-5 from their 20 overs, with Adam Zampa taking three wickets.

Usman Khawaja's first-ever T20 half-century got Australia's reply off to a good start, but quick wickets then fell in the middle of their innings before Maxwell's 26 off 15 balls handed them back the advantage.

In the end, the total was reached with nine balls to spare as Australia moved up to third in group two behind New Zealand and Pakistan, whom they face next on Friday.