The master batter had a few nervous moments before top-scoring with 71 in a meagre total of 198 all out, after captain Pat Cummins won the toss.
Bangladesh pace bowler Hasan Mahmud starred with 6-55, including the wicket of Smith, who skied a swat chasing runs with the tail. It was the 26-year-old's best Test figures in an innings.
Smith has still not scored a Test century against Bangladesh, the only one of the nine Test-playing nations he has played against where he has not achieved the milestone.
The rest of the Australian batters struggled as Bangladesh pace trio Taskin Ahmed, Ebadot Hossain and Mahmud bowled superbly on a surface that assisted the seam bowlers.
Ebadot (2-39) should have claimed Smith on two when he was dropped by Tanzid Hasan at third slip.
Bangladesh then lost a second review when Smith was given not out on seven after Ebadot was convinced he'd nicked one.
There was a sense Australia's No.4 had made a move towards the pavilion, but Snicko showed nothing on his outside edge.
Ebadot cleaned up Alex Carey (19) after lunch and Taskin castled Beau Webster (12) with an absolute beauty. Pat Cummins (nine) and Mitchell Starc (one) both nicked off to Mahmud before tea.
Smith made a statement when he launched veteran spinner Taijal Islam over the ropes and then through the covers in his first over of left-arm spin.
He had little support in conditions that suited the seamers.
Earlier the battles of Jake Weatherald and Marnus Labuschagne in Test cricket continued as Bangladesh struck early blows to have the hosts 4-74 at lunch.
Weatherald had an opportunity to enhance his chances of staying in the top order in front of a partisan crowd in Darwin, the city of his birth, but was unable to make the most of a start at Marrara Stadium.
It was no surprise when the 31-year-old edged impressive paceman Mahmud on the cusp of drinks to bring an end to a scratchy 23 off 37 deliveries.
Opening partner Travis Head (22) followed soon after, chopping on to Mahmud when he went around the wicket.
Ebadot had Labuschagne (1) edging to captain Najmul Hossain Shanto with an indecisive poke as his drought without scoring a Test century extended to 37 innings.
A horror shot by allrounder Cameron Green (13) on the stroke of lunch went straight to mid-wicket, another misadventure by a player who is yet to turn his promise into consistent runs.
The Test is the first played at the venue since 2004 and just the third in Darwin history after Bangladesh were the first visiting side in 2003.
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