Tasmania face a mammoth final-day run chase to keep their Sheffield Shield season alive, while Western Australia need ten wickets to do the same.
Openers Jordan Silk and Alex Doolan, both 20 not out, guided the Tigers to 0-54 at stumps on day three in Hobart.
The hosts need another 399 runs to win.
Sam Whiteman fell agonisingly short of a ton on Thursday as the Warriors declared at 8-283 in their second innings.
Whiteman was caught at gully for 93 off Gabe Bell, who was the pick of the Tigers' quicks with figures of 3-72.
Bell was on a hat-trick in the opening session at Bellerive Oval after trapping Cameron Bancroft (22) in front and bowling Josh Inglis for a duck in consecutive deliveries.
Bancroft hasn't done his chances of an Ashes call-up any favours, with his 22 following 27 in the first innings.
On familiar home turf of his Big Bash League side Hobart Hurricanes, D'Arcy Short smacked an unbeaten 61 from 69 balls batting at No.7.
Former Test wicketkeeper Matthew Wade claimed two lower order wickets, taking his season tally to four.
With ladder-leaders Victoria beating second-placed NSW, Tasmania and WA can stay in the mix for a top-two berth by claiming outright points.
The Tigers were dismissed for 197 in their first innings in reply to WA's 367.
