Tasmania require 316 runs to avoid an upset loss to South Australia and lock up hosting rights for the Sheffield Shield final.
Caleb Jewell (3) and nightwatchman Gabe Bell (0) were unbeaten at stumps on day two for the Tigers (1-8), who began their second innings chasing 323 for victory in Hobart.
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 (6-44) 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 (6-40), having put the Tigers into a tailspin at 3-27 on day one.
The 30 year-old made light work of the Tasmanian tail and ended the Tigers' innings when Jake Doran (52) 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 (4-36) was a willing co-pilot for McAndrew, dismissing Australian international Wade (20) 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 (2).
Allrounder Beau Webster (3-27) starred as Tasmania restricted the Redbacks to 175 in their second stand at the crease.
But it was spinner Jarrod Freeman (1-17) who closed out proceedings by enticing the most prolific South Australian Nielsen (53) into holing out to long on.
Fifth-placed South Australia are out of contention for the Sheffield Shield 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.
