The visitors were 123 for six at lunch, still trailing Bangladesh by 137 runs with Glenn Maxwell on eight and Matthew Wade on five at the Sher-e-Bangla National Stadium.
Off-spinner Mehedi Hasan bowled Smith for eight, an addition of just five to his overnight score, in the third over of the morning session after the tourists resumed on 18 for three.
Overnight batsman Matt Renshaw and Peter Handscomb put on a gritty a 69-run partnership for the fifth wicket, helping Australia past 100 before Bangladesh struck again.
Renshaw had survived a scare on 14 when he was given out lbw by the on-field umpire but the left-handed batsman reviewed the decision in his favour.
Bangladesh -- playing Australia in a Test for the first time in more than a decade -- were bowled out for 260 before their spinners made two quick strikes on day one.
Shakib and Mehedi Hasan have claimed two wickets each so far.
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