After hitting 128 against England in Bangladesh's opening match on Thursday, Tamim was the main man once again, but this time he lacked support and was unable to stop Australia taking control at The Oval.
While Tamim was rock solid, hitting his 95 off 114 balls with six fours and three sixes, Shakib Al Hasan was the next highest scorer on 29.
Pace bowler Mitchell Starc was Australia's most effective force with four wickets from his 8.3 overs.
Australia, whose final group match is against England in Birmingham on June 10, were the victims of one of the all-time great upsets when Bangladesh beat them by five wickets in a one-day international in Cardiff in 2005.
But it would be an even bigger surprise if Steve Smith's side fail to knock off the runs required to secure their first win of the tournament.
The main threat to Australia's ambitions could come from the weather, with rain forecast for the latter part of the day.
Rain had already ruined Australia's opener against New Zealand, which was abandoned on Friday, leaving them with no margin for error as they bid to qualify for the semi-finals.
Beaten by England last week, Bangladesh must win to keep their last four hopes alive.
Bangladesh captain Mashrafe Mortaza elected to bat after winning the toss on an overcast afternoon, but Tamim's initial flurry of boundaries was as good as it got for the Tigers.
Having put England's bowlers to the sword, Tamim was back in the groove, skipping down the pitch and driving the ball back past Josh Hazlewood for an emphatic four.
However, Hazlewood was in form as well after taking six wickets against New Zealand and he struck the first blow for Australia in the sixth over when he exposed Soumya Sarkar's leaden footwork, inducing an edge behind to wicketkeeper Matthew Wade.
Pat Cummins tempted Imrul Kayes to flick a short ball to Aaron Finch and, with Tamim taking a more cautious approach after those wickets, Bangladesh didn't score a boundary for 11 overs.
A productive period for Australia got even better when Moises Henriques had Mushfiqur Rahim dismissed lbw to reduce Bangladesh to 53-3.
Tamim finally started to hit out again, clobbering Bangladesh's first six and following that blow with two fours in the same Henriques over.
Having reached his 37th half-century in one-day internationals, Tamim watched from the other end as Travis Head trapped Shakib for 29.
Without Tamim, Bangladesh would have been in tatters, but he maintained his one-man show by blasting two sixes off Head.
Spinner Adam Zampa had replaced John Hastings in the Australia team and he took only two balls to make an impact, removing Sabbir Rahman for eight.
Zampa followed his opening wicket maiden by bowling Mahmudullah via a thick inside edge.
Tamim was on the brink of his second ton of the tournament, but his miscued hook off Mitchell Starc was caught by the diving sprawling Hazlewood.
Starc cut through the Bangladesh tail, bowling Mashrafe Mortaza and Rubel Hossain for ducks in successive deliveries, before seeing off Mehedi Hasan to make it four wickets in nine balls.