Australia's bowlers hit back in the final session to reduce Bangladesh to 124 for five in their second innings on the third day of an extraordinary first Test on Tuesday.
The home side, who hit 427 in their first innings, dismissed Australia for 269 after Adam Gilchrist hit his 16th Test century (144).
Bangladesh, 41-0 at tea, now have a lead of 282 runs over the world champions who will have a good chance of avoiding an embarrassing defeat if their bowlers strike early on Wednesday.
Bangladesh have won only one of their 42 Test matches since 2000, that victory coming over a depleted Zimbabwe side. They lost their two previous tests against Australia in 2003 by an innings.
Australia avoided the follow-on thanks to Gilchrist who batted superbly with the tail-enders to take his side from 93-6 to within 160 runs of Bangladesh's total. The left-hander hit six sixes and 14 fours.
Resuming at 145 for six, Australia lost Brett Lee in the morning session lbw to Mashrafe Mortaza for 15 before fast bowler Jason Gillespie gave Gilchrist good support.
Mohammad Rafique eventually had Gilchrist caught by Shahadat Hossain at deep square leg. The spinner captured the three wickets to fall after lunch, removing Gillespie (26) and Stuart Clark (0) for his seventh Test five-wicket haul (5-62).
When Bangladesh batted, first innings centurion Shahriar Nafees was bowled by Brett Lee on 33 with the score on 48.
Fellow opener Javed Omar (18) was quickly caught behind by Gilchrist off Gillespie to start a mini-collapse.
Skipper Habibul Bashar was run out for seven by a direct throw from Michael Clarke and Mohammad Ashraful (4) was the next to go when he was trapped lbw by Stuart Clark.
Aftab Ahmed was trapped lbw by Stuart MacGill on 21. Rajin Saleh (29) and Khaled Mashud (0) were not out at the close.
