The Alcohol.Think Again Western Warriors were skittled for just 67 in their first innings in reply to the Tigers' 9-431 (dec), headlined by a Matthew Wade century.
Asked to follow on, they were 5-176 at stumps - still behind by 188 runs.
Youngster Tom Rogers did the bulk of the damage for the home side, finishing with 4-9 from three overs after a quickfire 48 with the bat earlier in the day.
The Tigers' five-man pace battery proved a handful under overcast skies in Hobart.
Sam Rainbird and Andrew Fekete picked up two wickets each as WA were dismissed midway through the second session, having been 2-23 at lunch.
A shining light for the understrength Warriors was a second-innings 74 from opener Josh Philippe.
WA is missing eight players to Australian T20 or Test duties, including Shaun Marsh, Mitchell Marsh and D'Arcy Short.
Resuming at 5-327 on Saturday morning, the Tigers lost Wade (139) and allrounder Simon Milenko (78) inside the first four overs to debutant Liam Guthrie.
But bowlers Rogers and Rainbird put a young Warriors attack to the sword in an 81-run partnership.
Tasmania are second last on the table, but just eight competition points behind leaders Queensland.