Tigers paceman James Faulkner used a low-bouncing day four pitch to snare 5-56 as the Bushrangers were bowled out for a second innings 225, booking his side a place in the decider beginning on Friday.
Tasmania will have the chance to deliver champion Ricky Ponting his first silverware with his state in possibly his last season, while departing coach Tim Coyle can also be sent off with a third Shield title.
They came into the final round of matches in fourth spot, while the Bushrangers had been first, but all six teams had a chance to make the final.
Who Tasmania will play, and where, remained up in the air as Western Australia and Queensland battled it out in Perth.
A WA win, looking less likely as the day wore on, would mean the final is played in Perth.
A Queensland victory would mean the Bulls travelling to Bellerive if, as expected, their run quotient remained inferior tot he Tigers'.
A draw at the WACA would result in NSW travelling to Hobart to meet the Tigers.
Victoria were set 337 from 73 overs after Tasmania declared at lunch on 7-325.
But a collapse of 4-10 in 21 balls after they were 2-112 left them struggling at 5-122.
A partnership of 80 between David Hussey (48) and Peter Handscomb (33) threatened to set up a launch pad for the Vics to attack the target.
But a double strike from Faulkner after tea, when he bowled both batsmen, reduced the visitors to 7-207 and Ben Hilfenhaus (2-55) mopped up the tail.
Earlier, it was Ponting (86) and 20-year-old maiden century-maker Jordan Silk (127) who led Tasmania's charge from 1-137 overnight with a stand of 142 at close to five runs an over.
The former Test skipper tops the Shield run-scorers' list this season with 875 at 87.5.