Daniel Worrall (4/42) and Joe Mennie (3/27) were the pick of the quicks after the West End Redbacks sent the Tigers in on a green-tinged Blundstone Arena.
South Australia openers Jake Weatherald and Conor McInerney successfully navigated two overs before stumps but didn't add a run.
Matthew Wade top scored for Tasmania with 43 and was the second-last wicket to fall as he chased quick runs.
The Tigers lost two wickets in the each of the opening two sessions, and 6/82 in Tuesday's final session.
Veteran George Bailey scored 28 after last week handing the captaincy to Wade to focus on fixing his ailing batting.
Returning from national limited-overs duty, Ben McDermott scraped 18 but was out shortly after lunch, trapped in front by Nick Winter (2/57).
Kane Richardson picked up one wicket in a tight team bowling effort that kept the Tigers' run rate to 2.1 per over.
Tim Paine (16) edged Mennie to slip in his final hit-out before captaining Australia against India in the opening Test of the summer in Adelaide from December 6.
Worrall dismissed both Tigers' openers in the morning session and took the last wicket of tailender Gabe Bell 20 minutes before stumps.
His four wickets come after a career-best 10-wicket haul on return from injury against Western Australia last week.