The run-chase total also comes as Australia's second-highest fourth-innings target for a Test in Asia, meaning the picture is starting to look as bleak as it seems, unless its batsmen can turn things around.
All-rounder Shakib Al Hasan took 5-85 to help the hosts dismiss Australia for 244 shortly into the second session on the fourth day.
Bangladesh won the match by 20 runs. A similar triumph in next week's second and final test in Chittagong would result in Australia tumbling to No 6 in the world rankings. Australia became the fifth team to have been beaten by the Bangladeshis in Tests so far (the other four being Zimbabwe, Sri Lanka, England and the West Indies).
Matt Renshaw was batting on six at stumps with skipper Steve Smith on three. I hope we will get a wicket that will help us to win the series, ' he added.
The lower order has got better. The push for the team to become more competitive overseas has resulted in the focus on grassy wickets in their domestic competition, but Tamim said it could be to the detriment of developing a strong home record.
"Well done Bangladesh. Special effort to beat Australia".
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Mushfiqur Rahim's all-round show: Mushfiqur made a decision to move in with a spin-dominated attack, picking Shakib, Taijul Islam and Mehidy Hasan.
"He said it is going to be pretty hard sitting at home watching, he hasn't done that for three or four years so he's a big member around the group".
Matthew Wade (5) lasted just nine balls, while Glenn Maxwell's (23) departure had the visitors staring down the barrel of a 100-run plus first-innings deficit.
"So we had the belief". Only two of Australia's top six - David Warner and Steven Smith - have played more than 50 Tests, while Tamim Iqbal, Shakib Al Hasan and Mushfiqur Rahim have each played more than 50 Tests for Bangladesh.
"There is a lot of room for improvement". And he intelligently rotated the bowlers, especially spinners, and the field placements were accurate. They did miss some [catches] but it can happen. "Obviously after this Test they'll show a lot more respect", he said. After putting up 260 runs in their first innings, Bangladesh bowled out Australia for 217, taking a lead of 43.
After resuming on 75, Warner raced to triple figures before being trapped lbw by Shakib on 112.