Swing bowler Daniel Worrall claimed the wicket of Jake Doran to have the Tigers three down at stumps, but the Tigers claimed honors on the second day on what appears a tricky Hobart wicket.
South Australia lost 7/37 in Wednesday's second session with skipper Travis Head (49) top-scoring for his side.
The visitors were solid at 3/77 at lunch but lost wickets cheaply after the break.
Tasmanian debutant Alex Pyecroft (3/36) had Jake Lehmann (28) edging to slip with Tom Cooper, Alex Carey and Joe Mennie falling in quick succession.
Head was given out cutting Riley Meredith (1/23) to wicketkeeper Tim Paine as South Australia posted a first-innings total of 136 in reply to Tasmania’s 185.
In his return from national limited overs duty, Ben McDermott hit a quick-fire 54 to put the hosts in command.
The Tigers finished the day at 3/120, with Jordan Silk (49) and George Bailey, who is yet to score, at the crease.
In-form Redbacks bowler Worrall (3/32) has all three wickets for SA in the second innings.