Opener Conor McInerney (11) and veteran Callum Ferguson (five) will resume at the crease for SA on Friday with the visitors 1/16 trailing the Tigers by 386 runs.
Left-hander Jake Weatherald was the late victim nearing stumps adjudged LBW for no score.
Tasmania’s Jordan Silk notched his sixth first-class ton to press the Tigers’ advantage on Day Three as the hosts declared at 8/353 (dec) holding a 402-run lead.
Silk shared a 93-run stand with veteran George Bailey (63) while Australian Test captain Tim Paine also contributed with an unbeaten 47.
The pair of Silk and Bailey almost batted through the morning session after resuming at 3/120 but Bailey was trapped in front by Joe Mennie (2/70) on the last ball before lunch.
Redbacks paceman Daniel Worrall finished as the pick of SA’s bowlers with 3/83 to go with four first-innings wickets.
SA skipper Travis Head took the final two wickets of Tasmania’s innings while left-arm paceman Nick Winter (1/60) was the Redbacks’ remaining wicket-taker.
STUMPS ⌛— West End Redbacks (@WestEndRedbacks) November 29, 2018
McInerney 11* and Ferguson 5* survive and we'll reset for the final day of play
SA 1/16 need 387 to win
Scorecard 📊: https://t.co/EVKrwpRUYG #SheffieldShield #TASvSA pic.twitter.com/q4n1ilWvxP