George Bailey's unbeaten century helped Tasmania post a commanding total of 433 for 8 before they declared on the second day in Hobart.
Resuming on 278 for 3, Bailey and Ben Dunk pushed the score past 300 before Dunk was dismissed by Jack Wildermuth for 142.
Bailey, however, ensured there was no let up in momentum and, despite minimal contributions from lower-order batsmen, he kept scoring at a healthy rate. He put on 48 runs for the eighth wicket with Xavier Dorthy and remained unbeaten on 148 off 190 balls when Tasmania declared.
Tasmania had a wobbly beginning to their reply when they lost Scott Henry to seamer Andrew Fekete, but Sam Heazlett and Matt Renshaw put on 90 runs for the second wicket. Fekete, however, struck a blow late in the day too, to remove Renshaw for 37, but Heazlett's unbeaten 69 on first-class debut held the visitors' innings together.