Tanzid raised his hundred with a single off Nathan Lyon from 188 deliveries but, after a patient and resilient innings, added just one more run before lofting a ball from the veteran Australian spinner to Mitchell Starc at long-off soon after.
He shared two big and important partnerships to set the No 9-ranked Bangladesh on course for a sizeable first-innings lead, combining with Mominul Haque (49) in a 102-run second-wicket stand and adding 93 with skipper Najmul Hossain Shanto for the third.
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Shanto went on to score 84 from 126 deliveries before becoming one of three wickets to fall in a four-over period soon after Australia took the second new ball.
Bangladesh resumed on Friday at 96-1, 102 runs behind in the first innings after dismissing Australia for 198, and finished day two with a 153-run lead and four wickets in hand.
In their first Test on Australian soil since 2003, the Bangladesh players were just as disciplined with the bat as they were with the ball on the opening day.
Mehidy Hassan Miraz (32) and Hasan Mahmud (13) shared an unbroken 43-run partnership for the seventh wicket to get Bangladesh to stumps in the kind of position few expected ahead of the series.
The reunion of Australia's so-called Big Four, pacemen Pat Cummins, Josh Hazlewood and Mitchell Starc, alongside veteran off-spinner Nathan Lyon, has so far been blunted with the visiting batters frustrating Australia in the warm, tropical conditions in the Northern Territory capital.
Seamer Starc was involved in a heated exchange with Bangladesh batter Miraz after the pair nearly collided during the bowler's follow-through.
"It's my follow-through not your follow-through, get off the wicket!" Starc said, before the umpires separated the two players.
The two-Test Top End series begins a demanding 12-month schedule for Australia that will feature 20 Test matches, including tours of South Africa, India and England.
Watch the three-Test series between England and Pakistan live on Sky Sports Cricket from August 19. Stream cricket and more sport contract-free with NOW.
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