Victoria grabbed the last four Tasmanian wickets for 13 runs to bowl the visitors out for 198 halfway through Sunday's final session and post the victory.
Victoria remain fourth in the standings, but they can make the final by beating Queensland and New South Wales outright in the remaining two matches and hoping both rivals are kept pointless in other matches.
It was Victoria's 14th outright victory at the Melbourne Cricket Ground from their past 18 matches (one loss).
They earned their win the hard way and only broke the back of the Tasmanian resistance by removing Michael Bevan, who was headed for a fourth successive century until Shane Warne had him caught at slip.
Bevan's dismissal for 86 -- after 144 in the first innings -- prompted a swift close, as paceman Shane Harwood (3-47) cleaned up the tail with 3-8 in 15 balls.
Bevan's remarkable season has now yielded 1,109 Shield runs, but aside from openers Travis Birt (43) and David Dawson (17), no other Tasmanian reached double figures.
Warne, who took 2-37 in the second innings, is expected to play against Queensland before the Australian Test series in New Zealand in March.