Western Australia declared its innings closed at 562 for six with wicketkeeper Ryan Campbell compiling his ninth first-class century and top-scoring with 134 on Thursday.
In reply, Tasmania was 192 for three at stumps -- still 371 runs shy of overhauling Western Australia's first-innings total.
All-rounder Shane Watson was an unbeaten 51 while former West Australian Michael Dighton was 63 not out as Tasmania sought the 221 runs needed to avoid the follow on.
"It's not impossible to take wickets, but it is hard work," Tasmanian coach Brian McFadyen said.
Starting the day on a commanding 345 for four, Western Australia scored freely before declaring 25 minutes after lunch.
The decision came after all-rounder Kade Harvey celebrated his maiden first-class century.
Campbell's century came off 106 balls with 12 fours and two sixes before he was caught at cover by Watson off left-arm orthodox spinner Xavier Doherty.
Western Australia then hobbled Tasmania's run chase by taking 52 for two before tea with opener Jamie Cox out for 24 and left-hander Scott Mason dismissed for 19.
Hobart (day two): Tasmania 192-3 (M. Dighton 63 no, S Watson 51 no; J. Taylor 2-67, B Edmondson 1-19) v Western Australia 562-6 decl (R Campell 134, M North 118; G Denton 2-122, A Downton 2-144).
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