In just his second Test match, the 25-year-old left-hander's brilliant 101 put the Tigers in position to push for what would be their greatest win in long-form cricket.
There is still a long way to go, but Bangladesh went to stumps on day two at 6-351 after recovering from a mini-collapse of 3-11 when Australia took the second new ball.
Steve Smith took the first three catches after tea at second slip to equal Joe Root with 218 catches, the most in Test history by a fielder.
Josh Hazlewood, Mitchell Starc and Pat Cummins all struck after tea with the new cherry but allrounder Mehidy Hasan Miraz (32 not out) and fast bowler Hasan Mahmud (13no) could not be budged, although Cameron Green dropped Mehidy off the last ball of the day to sum up his Test so far.
Australia allrounder Beau Webster said Bangladesh "batted beautifully".
"We tried a few different plans ... wide, straight, spin and some bumpers from Marnus (Labuschagne) at the end there," he said.
"We are going to have to come up with some more plans. With the quality in our dressing room I am sure everyone is still looking at a way to win this game of cricket."
Left-hander Mominul Haque (49) and Tanzid added 102 for the second wicket with poise and flair after the visitors began proceedings on Friday at 1-96, in replay to Australia's 198 all out.
Captain Najmul Hossain Shanto (84 off 126 balls) dominated from the start of his knock to continue the momentum against an Australian attack that was accurate, but lacked venom.
Tanzid has cemented himself as a regular in white-ball cricket at the top of the order but against a world-class attack he appears set for an extended run in Tests too.
On 96, he tried to slap Nathan Lyon over cover to bring up his century and lobbed the drive close to deep mid-off. A push past Lyon in the next over secured an extraordinary ton, before he was out lofting down the ground.
"I can't describe it in words but it is very special for me," he said of the achievement.
The dashing opener's driving through cover and point was exquisite and his shot selection was outstanding after a shaky start late on the opening day.
The early conditions provided bounce, carry and seam, but Bangladesh's batters were far more judicious than Australia had been with their shot selection.
One square cut by Shanto, where he stood on his toes and placed a Starc delivery to perfection to the boundary, summed up the methodology of the visitors.
The captain waited for the ball and hit it right under his eyes, rather than reaching out for it as several Australian batters had done.
The century partnership for the second wicket was brought up with the shot of the match, when Tanzid danced down to Beau Webster and lofted his drive straight over the mid-off boundary.
After a first day that was regarded as the best single day of Test cricket played by Bangladesh, against a full-strength Australia, the challenge was always going to be to back it up.
Mominul, 34, took up that challenge. The No.3 has been a wonderfully consistent player in the Test arena and reached double figures for his 17th consecutive innings, dating back to April of last year.
He was on the cusp of his eighth half-century in that period but nicked Hazlewood to fall one run short.
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