The result leaves Australia with two points after two games, knowing that they will need a win over England to be safe from group stage elimination regardless of the other results unless more matches are rained off or end in a tie.
It meant both of Australia's games in the tournament so far have been abandoned due to rain, they getting a point against New Zealand from a disadvantageous position and then this share of spoils with Bangladesh.
Smith was quite critical of his bowlers after the match against New Zealand, where Australia were extremely fortunate to leave with a point, after the match was abandoned.
The "no result" benefited Bangladesh as a loss against Australia would have knocked them out of the tournament. On the bright side for Smith, his bowlers were more effective against Bangladesh after struggling to find their rhythm in the New Zealand match. "We hit some good areas early on and challenged the defence of Bangladeshi batsmen", Smith said.
Starc came within inches of claiming a hat-trick, nearly bowling last man Mustafizur Raham with a yorker, before settling for a triple-wicket maiden and bowling Mehedi Hasan in his next over.
Tamim Iqbal's 95 was the only solace for Bangladesh with the opener falling just short of scoring back-to-back hundreds for the second time in two years.
Bangladesh, who had to avoid defeat to keep alive any hopes of qualification from Group A, were skittled for 182 but Australia's likely stroll to victory was curtailed by bad weather at 83-1. Bangladesh won the toss and opted to bat first on a placid wicket, where the sun was beating down hard.
To the delight of a partisan crowd dotted with Bangladesh's green and red, he launched Henriques over wide long-off for six, then pulled his next ball for four.
Neither team could come away from their respective opening games with a win, making this, pretty much, a must-win for both sides.
Steve Smith's side were chasing 183 to beat Bangladesh at The Oval when persistent drizzle forced the players from the field.
Josh Hazlewood snared the wicket of Soumya Sarkar (3) with a length delivery before Imrul Kayes (6) was too slow for Pat Cummins pace off the pitch, sending an easy catch to cover.