Nightwatchman Nathan Lyon lasted five balls before being trapped LBW by Shakib Al Hasan for a duck in the same over.Australia will resume with Renshaw unbeaten on six and skipper Steve Smith on three.
It was a disastrous end to the day for Australia, who had been well-placed after skittling Bangladesh with time to spare, led by three wickets in two overs from speed demon Pat Cummins.
But Lyon insisted that while Bangladesh had the momentum, the game remained in the balance.
"It's not ideal losing three wickets but that's the game ... now it's our chance to fight back and really test ourselves in these conditions," he said.
"We've got two very, very good batsmen (at the crease) ... we're just going to have to work hard, bat well and bat long in partnerships.
"There's no demons in that pitch as yet so it's a good opportunity for our batters."
Lyon and recalled left-arm spinner Ashton Agar spun through the Bangladesh middle-order and tail to finish with a combined six wickets.
Part-time spinner Glenn Maxwell earlier made the key breakthrough, bringing a 155-run partnership to an end when he had Tamim Iqbal caught by David Warner at backward point on 71.
Lyon then claimed the big wicket of Shakib Al Hasan, who was caught by Smith at first slip on 84 off a delivery which spun sharply away from the left-hander.
It was a welcome change for Lyon, who was hit for six three times by big-hitting opener Tamim and went to tea with 1-59.
The partnership between danger men Shakib and Tamim was much-needed for Bangladesh, who were left reeling at 3-10 off four overs after a lethal spell from Cummins.
Playing just his fourth Test in a hugely promising but injury-affected career, Cummins was a revelation despite the draining 75 per cent humidity in Dhaka.
