Tanzid Hasan became the first Bangladeshi to score a test century in Australia as the visitors dominated to reach 286-3 at tea on the second day of the first test in Darwin on Friday.
Led by a superb 101 by opener Tanzid and an entertaining 79 not out from captain Najmul Hossain Shanto, Bangladesh led the hosts by 88 runs at the break with seven wickets in hand.
Mushfiqur Rahim (26 not out) was alongside Najmul as the Bangladesh batsmen ground down the Australian attack.
Tanzid batted brilliantly in perfect conditions in the Northern Territory capital as Bangladesh chase a maiden test win in Australia at the third attempt.
Playing just his second test, the 25-year-old looked in complete control against the Australian attack to make a piece of history.
He had a let-off on 62 when he edged Nathan Lyon to first slip, where the usually reliable Steve Smith couldn't hold on to a sharp chance.
Tanzid brought up his ton with a push through mid-off off Lyon midway through the second session.
He took 188 balls to reach triple figures, hitting eight fours and a massive six off Lyon.
He perished soon after, trying to hit Lyon out of the ground but only finding Mitchell Starc at deep mid-off.
Bangladesh would have been hoping for a good start to the morning after a superb opening day when they bowled the much-vaunted Australians out for 198.
Tanzid and Mominul Haque did just that, starting the day at 96-1 and batting comfortably through the first hour's play.
The Australian bowlers were much improved on Thursday's efforts but the Bangladesh pair played patiently, taking singles when on offer and waiting to pounce on the rare bad balls.
Tanzid brought up his half-century shortly before the drinks break, reaching his 50 off 102 balls.
Mominul looked certain to join Tanzid in reaching the milestone, but on 49 he tried to punch a Josh Hazlewood ball through the off-side, only managing a thick edge to wicketkeeper Alex Carey.
The pair had put on 102 runs and took Bangladesh to 138-2, 60 runs behind the Australian first innings.
Skipper Najmul joined Tanzid at the crease and immediately increased the scoring rate against a tiring Australian attack.
That accelerated even further when Mushfiqur joined his captain following Tanzid's dismissal.