Australia need another 156-run to win with eight wickets remaining in their first Test match against Bangladesh.
The visitors scored 109 for 2 in 30 overs after third day’s play in Mirpur’s Sher-e-Bangla National Stadium on Tuesday.
Earlier, Australia lost opener Matt Renshaw and Usman Khawaja in a disastrous opening to their run chase of 265 in the final session of day three in Dhaka.
Renshaw was the first to go, lbw to Mehedi Hasan for five, before Khawaja completed a forgettable match with the bat, sweeping to Shafiul Islam off Shakib Al Hasan to be caught for one.
Opener David Warner looked to be Australia's key man, racing to a half-century to bring the runs required to under 200, while captain Steve Smith narrowly survived a stumping appeal as he eased his way into his innings.
Bangladesh had been bowled out for 221 shortly after tea, with Nathan Lyon taking 6-82 to finish with nine for the match.
Lyon collected the final two wickets to fall 20 minutes into the final session, but a respectable batting effort by the Tigers - led by Tamim Iqbal's 78 and their captain Mushfiqur Rahim's 41 - means the tourists will require their second-highest successful run chase in Asia if they are to avoid what would be a humiliating Test defeat.