Bangladesh were 205 for eight at the interval, having lost five wickets while adding 72 runs during the post-lunch session.
Bangladesh defeated Australia by 20 runs to go 1-0 up in the 2-Test series by creating a historic win.
Glenn Maxwell was unbeaten on 8 and Matthew Wade was batting on five at the interval, with just the tailenders to come.
Australia resumed on 109 for two in pursuit of 265 with Warner and Steve Smith at the crease, and the pair quickly brought up their 100 partnership.
Australia have been known to be a team full of bold and brash players but Bangladesh have a more understated approach.
Shakib cracked 84 in the first innings, which doubled his feat of smashing a half-century and grabbing 10 wickets in a Test match.
Peter Handscomb, Matthew Wade and Ashton Agar were dismissed before lunch and Glenn Maxwell (14) went from the first ball after the interval, Shakib bowling the unsafe right-hander when he went back attempting a cut.
But Smith settled himself and shrugged off the early nerves while Warner played what is already one of his best - if not the best - knock in such conditions.
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Shakib first trapped Warner leg-before for 112 and, four overs later, had Smith caught behind for 37 to pile the pressure back on Australia.
But for all their dominance at home, Australia showed they remained a fragile side overseas who could be easily exposed by quality spinners.
"A great effort by the boys, especially Shakib and Tamim [Iqbal] were outstanding", Mushfiqur said.
The 30-year-old further revealed that at home, Bangladesh have the confidence that they can beat any side.
Peter Handscomb, who had displayed admirable grit in the series against India, cut a short ball from Taijul but the edge flew to first slip where Soumya Sarkar produced a brilliant reflex catch on the second attempt to give Bangladesh hope. Shakib Al Hasan was the architect of Bangladesh's win as they clinched the series opener by 20 runs.
Cummins belted offspinner Mehedy Hasan for two sixes in one over to reduce the deficit but it was all over when Taijul Islam trapped Josh Hazlewood lbw for a duck. "It was pretty hard batting here in the second innings and I thought we did pretty well to get 240 in the end".
Quite the turnaround from a nervy first innings showing when six batsman were out for single-figure scores, leaving the Australians wobbling at 124-7 until Ashton Agar and Pat Cummins wrestled their way to the 200 mark.