Tanzid Hasan made his first Test century and Bangladesh went past Australia's first innings before tea on day two in Darwin, reaching 3-286 and a lead of 88.
Tanzid made 101 from 197 balls with eight fours and a six. He is the second Bangladesh batter to score a Test century against Australia. Shahriar Nafees made 138 at Fatullah in 2006 and nobody had done it since.
Tanzid added 102 for the second wicket with Mominul Haque, who was out for 49, and the pair took Bangladesh through the first session on Friday for the loss of one wicket. The six came off Beau Webster, straight down the ground.
Najmul Hossain Shanto was 79 not out at tea. The Bangladesh captain brought up his fifty off Nathan Lyon and had added 55 for the fourth wicket with Mushfiqur Rahim by the break.
Australia were bowled out for 198 in 53 overs on Thursday, their lowest Test total against Bangladesh, with Hasan Mahmud taking a career best 6-55. Steve Smith's 71 was the only score above 23.
Mitchell Starc had 1-50 at tea. Australia have taken three wickets since Bangladesh began their reply late on Thursday, and Pat Cummins has been through his front-line bowlers and his all-rounder without breaking the innings open.
This is the third men's Test at Marrara Stadium and the first since 2004. It is Bangladesh's first Test tour of Australia in 23 years.
Bangladesh have seven wickets in hand and two and a half days to bat into. Australia's problem is no longer the 198. It is that the pitch on which they made it has not misbehaved since.
