Both sides lost their opening matches in the five-team group so knew a victory was essential if they wanted to maintain realistic hopes of reaching the semi-finals.

The Australians won the toss and opted to field at Bangalore's M.Chinnaswamy Stadium with Bangladesh posting 156-5.

This represented something of a recovery after Shane Watson removed both Soumya Sarkar and Sabbir Rahman in the early going to leave Bangladesh on 25-2.

Mahmudullah finished unbeaten on 49 in the total with spinner Adam Zampa taking the rest of the wickets to finish with figures of 3-23.

In response, Australia looked like they would cruise to their target as Watson and Usman Khawaja made it to 62-0.

A stream of wickets then fell, though, although the Australians were able to make it over the line as they search for a first World Twenty20 title.

Khawaja's effort proved key as he made 58 from 45 deliveries.

The victory puts Australia third in the group with the top two progressing, while Bangladesh are last.

In the women's competition, Australia were not as fortunate as they lost to New Zealand by six wickets in Nagpur.

The Kiwis restricted their opponents to 103-8 and then chased down the target from 16.2 overs.

New Zealand now have three wins from three at the top of Group A, with Australia second after a first defeat.