Tamim Iqbal scored his second half-century of the match as Bangladesh consolidated their lead over Australia on the third day of the first Test on Tuesday.
The hosts reached 133-3 at lunch to lead Australia by 176 runs on a turning pitch at Dhaka's Sher-e-Bangla National Stadium.
Tamim, who made 71 in the first innings, was 76 not out at the break after Bangladesh resumed play on 45-1.
Skipper Mushfiqur Rahim was on 25 at the interval, with Bangladesh seeking their first-ever win over Australia in what is only their fifth meeting in a Test.
Off-spinner Nathan Lyon took both the wickets to fall in the morning, trapping nightwatchman Taijul Islam lbw for four and forcing Imrul Kayes to edge a catch to David Warner at second slip for two.
Mushfiqur hit Lyon for a four and six in the bowler's successive overs during his unbroken 66-run partnership with Tamim for the fourth wicket.
Tamim, unbeaten on 30 overnight, struck Pat Cummins for two fours in the first over of the day before surviving a strong lbw appeal at 42.
Australia reviewed the not out decision by on-field umpire Aleem Dar but in vain.
The left-hander dispatched Ashton Agar to backward point for four to complete his second fifty of the game off 109 balls.