Travis Head's ninth first-class fifty lifted South Australia to 4 for 191, after their bowlers had restricted Tasmania to 291 in the morning.
Head added 75 runs for the third wicket with Tom Cooper, who made 26, as they helped the team recover from a shaky start which saw both their openers dismissed inside 22 overs.
Phillip Hughes, who had blasted 204 in the previous game against Western Australia, failed to get going this time, and was caught by Luke Butterworth off Clive Rose in the 12th over. Hughes' opening partner Michael Klinger, who too had notched a century in Adelaide, lasted slightly longer, hitting two fours as he made his way to 21, but he was trapped lbw by Xavier Doherty, leaving South Australia at 2 for 61.
But Head and Cooper counterattacked by smashing a total of 20 fours - 16 of those struck by Head - as the pair batted out 23.3 overs, but Butterworth eventually made the breakthrough and removed Cooper in the 45th over. Head carried on, and looked set to score his maiden first-class ton, but fell two runs short as he was caught behind by Tim Paine, to give Butterworth his second scalp of the day.
Callum Ferguson and Johan Botha batted out the remaining 7.5 overs of the day to leave South Australia trailing by 100 runs heading into day three.
Tasmania, who were 6 for 226 when the day began, were earlier helped by handy contributions from tailenders Doherty and Rose, who took the team to a respectable total.