Openers Caleb Jewell (24 not out) and Mac Wright (15 not out) had the Tigers 0-47 at stumps on day two at Bellerive Oval in pursuit of a victory target of 325.
Sixteen wickets fell on Friday, with Tasmania losing 5-23 after resuming their first innings at 4-52 before Victoria made 193 all out in their second dig.
Victoria's quicks Fergus O'Neill (3-17) and Sam Elliott (3-22) did most of the damage.
Elliott started the morning carnage when he trapped Charlie Wakim (15) lbw, before O'Neill bowled Test allrounder Beau Webster (five) three overs later.
Australia's short-form spinner Matt Kuhnemann top-scored for Tasmania with 23 after being sent in as a nightwatchman the previous evening.
Victoria were under the pump early, with first innings century maker and leading Shield season run scorer Sam Harper gone in the second over for a duck.
Wickets fell regularly, with Peter Handscomb (47) the only member of his side's top six to put up any real resistance.
He shared a 50-run partnership with O'Neill (44) but was out caught in the gully off the bowling of Riley Meredith.
Gabe Bell finished the best of the Tasmanian bowlers with figures of 3-40 that included the scalps of Victoria's top three.
"That last hour was crucial and being none down at stumps. We think the pitch is only going to get better as the game goes on," Bell said.
"If we can get through to lunch with minimal damage, we'll have a fair bit of confidence going into the back end of the day."
Top-placed Victoria have already locked-up a spot in the final, while a loss in the penultimate round would be a big blow to fourth-placed Tasmania's hopes of qualifying for the decider.
Queensland, South Australia and NSW are all in the running to make the final.
14°C