Some inspired spin bowling from rookie Todd Murphy saw Tasmania battle their way to 7-170 at stumps, a lead of 191.
In just his second first-class outing, right-armer Murphy followed up his four-wicket first innings haul with 3-43.
Among his scalps were Tasmania's dangermen Matthew Wade and Ben McDermott, with the pair briefly looking likely to build a handy lead.
But the 62-run third-wicket stand ended when McDermott was caught on the boundary for 21, and Wade was then dismissed at first slip for 50 ending his 87-ball knock.
Tasmania lost 4-19 and were in danger of completely capitulating at 6-105 only for allrounder Tom Andrews to hit a quickfire 40 off 49 deliveries.
That Andrews was run out in an extremely tight decision was emblematic of Tasmania's change of fortunes in a match they largely dominated for two days.
Middle-order batter Jordan Silk ended unbeaten on 22 after a gritty 96-ball stay at the crease.
With only South Australia out of contention, both sides went into the penultimate fixture with two wins apiece and vying for a spot in the final at the end of the month.
After a significantly disrupted season, points will be divided by matches played and Victoria, having played fewer matches, are at a slight advantage over their opponents.
Victoria opened day three at 4-210 and still with work to do to haul in Tasmania's 355, ultimately declaring 21 runs in arrears at 7-334.
The partnership of Travis Dean and Sam Harper continued to blossom and only ended at 187 when the latter was trapped plumb lbw for 93.
Dean fell just short of his highest first-class score when he was bowled for 146, having reached three figures late on day two.
Andrews picked up both wickets and returned the team's best figures with 2-53.
