The visitors went to stumps on day one at 3-18, having earlier bowled out Bangladesh for 260 with a disciplined performance in oppressive heat and humidity.
The opening Test will be the first between the two countries since Ricky Ponting's side toured Bangladesh in 2006, clean-sweeping the series 2-0.
"It's not ideal losing three wickets, but that's the game".
Warner was given out LBW off the bowling of Mehedi Hasan in the fourth over but quickly reviewed the decision, with replays showing the ball had clearly hit his bat first.
With two left-handers at the crease, Australia captain Steve Smith pressed off-spinner Nathan Lyon into service but Shakib and Tamim looked fluent against the slow bowlers. Shane Warne is the only Australian spinner to have now claimed more Test scalps than Lyon.
While Tamim Iqbal made 71 runs, Shakib hit 84 before falling to Lyon.
Lyon needs three wickets to become the eighth Australian to 250 in Tests. It is to be noted that none of the members of the Australian cricket team, who resolved their long-standing pay dispute with their cricket board recently, have played a Test against Bangladesh in the past. Facing the spin-heavy attack, they held their own with both bat and ball and will now look to draw on that experience in Bangladesh, where the pitches are expected to be worse.
As recently as the lead-in to Australia's tour to India earlier this year, where the 29-year-old pocketed his career-best return of 8-50 in the second Test at Bengaluru, questions were aired about his potency on Asian pitches, against the game's most accomplished wranglers of spin bowling.
Herath has claimed nearly 70 per cent of his wickets on home tracks in Sri Lanka while Ashwin was proved even more dominant in familiar climes with greater than 71 per cent of his victims falling on Indian soil.
They have spinners who will challenge Australia's defensive techniques and patience, and one of those is also the world's best Test allrounder: Shakib Al Hasan.
Nasir Hossain is playing a Test after a two years while pacer Shafiul Islam also returned to the fold.
"I've always said that I'm not about personal success but I woke up to a message from my mum and dad", Lyon said. At least we hope it's a photo shoot and he's not just forgotten his gloves, pads and helmet And one final warning before we leave you to it - don't be alarmed if Mitchell Johnson, David Warner and coach Darren Lehmann turn up at the beach while you're sunbathing. There was more damage in Cummins' next over as the quick found an inside edge to remove Imrul Kayes caught behind for a duck.
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