A 179-run-partnership between former one-day international Michael Bevan and young opener David Dawson took Tasmania to 196 for one before pacemen Shaun Tait and Paul Rofe tore through the middle order with the second new ball on Tuesday.
At one stage in the final session Tasmania lost 5-7.
Tait troubled the home side with pace and movement in taking 4-61, while Rofe claimed the wickets of Tasmanian captain Dan Marsh and wicketkeeper Sean Clingeleffer with consecutive balls.
The collapse reduced the effect of Bevan's flashy 106 - his second century in as many games for his adopted home state.
Dawson scored a painstaking 73 in more than five hours from 243 balls after Marsh won the toss.
In Hobart (day one): Tasmania 240 for 7 (M. Bevan 106, D. Dawson 73; S. Tait 4-61) vs South Australia.