123 (Doran 52, McAndrew 6-44, Doggett 4-36) and 8 for 1 need 316 more runs to beat South Australia 271 and 175 (Nielsen 53, Webster 3-37, Carlisle 3-42)
Tasmania require 316 runs to avoid an upset loss to South Australia and lock up hosting rights for the Sheffield Shield final.
After being set 323, an upset Matthew Wade was dismissed for a duck in the penultimate over of the day after the umpire adjudged the Australian international touched Jordan Buckingham's delivery as he shouldered arms.
Paceman Nathan McAndrew was chief agitator for the Redbacks earlier on Tuesday. He helped the visitors skittle their ladder-leading hosts for 123 after they lost the toss and managed 271 themselves on day one.
McAndrew finished the first innings just shy of his career-best bowling figures (6 for 40) having put Tasmania into a tailspin at 27 for 3 on the first evening.
He made light work of the Tasmania tail and ended the when Jake Doran nicked him to wicketkeeper Harry Nielsen. Doran had been the one Tasmanian to make a fist of things on a bowler's wicket and one of only three to reach double figures with the bat in the first innings.
Fellow quick Brendan Doggett was a willing co-pilot for McAndrew, dismissing Wade lbw on the first ball of the day. Doggett later sent down a pearler of a delivery that swung back into middle stump and dismissed Kieran Elliott.
Allrounder Beau Webster starred as Tasmania restricted the Redbacks to 175 in their second innings.
Spinner Jarrod Freeman closed out proceedings by enticing Nielsen into holing out to long on after a half-century which carried the lead over 300
Fifth-placed South Australia are out of contention for the final but a win could deny Tasmania the chance to host the decider next week pending other results. Tasmania will likely meet the winner of Western Australia's clash with Victoria in the final, though NSW remain a mathematical chance of qualifying if the game in Melbourne ends in an unlikely draw.