Steve Smith waited until the 35th over to bring legspinner Adam Zampa, who replaced John Hastings from their opener against New Zealand, into the attack.
Tamim looked on song at the other end but he and Shakib, who was dropped by Glenn Maxwell at point on 11, became watchful and the run rate dropped to around 3 per over.
Defeat was staring Bangladesh in the face. The quest for a place in the semi-finals begins now for both the teams as they look to register their first victory in this year's edition of the Champions Trophy. "It's a pretty quick tournament".
"Guys were a little bit concerned at the time, and didn't really know what to do", said Smith.
Security was heightened for Sunday's India vs Pakistan match at Edgbaston in Birmingham with both teams observing a minute of silence before play.
Australia needs 138 to win from 42 overs.
This gesture of the player makes Bangladesh somehow being upset.
Australia might have to beat England on Saturday to advance to the semifinals.
Theresa May Announces Plan To Form Government After Queen's Approval
That did not help May, who had overseen cuts in police numbers during six years in her previous job as interior minister. May called the election called in a bid to strengthen her mandate ahead of European Union exit talks.
· Australia won six consecutive ODIs at The Oval between 1999 and 2010 but have subsequently lost their most recent two games there.
"The game was totally in favour of the Australians and we got quite lucky", the skipper added.
"It's just being given the time to get some consistency back".
"England are probably expecting themselves to win and have been talking themselves up in the media".
Captain Mashrafe Mortaza commented after the game: "As I said earlier, Australia were unlucky today". Mortaza also conceded Bangladesh must be more ruthless when they have a chance to kill off opponents.
But the left-armer said he was still happy with the progression of the bowlers through the tournament, and hoped their best was to come. "With eight batters, we are in a great position to score 330, 340". Find us on Facebook too!
"All of us have to tell our security team where we're going to be and check back in when they return to the hotel. For us, it's about just being diligent with everything that we do and continuing the tournament as usual".
"Following last night's incident all team hotels went into lockdown and teams, match officials and staff were all quickly accounted for", the global governing body said.
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