Tasmania were dismissed for 209 in their second innings earlier on Friday, with Peter Handscomb the improbable star for the Vics.
The home side's skipper claimed five catches in the innings, tallying nine for the match to eclipse the previous Shield mark for a non-wicketkeeper by two.
Victoria wasted no time as they began their second innings, reaching 1-78 off just 19 overs by lunch.
Travis Dean followed up his first-innings century with a rapid-fire 47 at better than a run a ball, before being dismissed just before the end of an elongated first session.
James Seymour was unbeaten on 25 while Handscomb was two not out.
Tasmania resumed on day four at 7-170 at stumps, a lead of 191, and advanced to 209 before they were dismissed.
The last recognised batter, Jordan Silk, reached 42 and looked capable of extending Tasmania's lead to a more challenging target only to edge Jon Holland for Handscomb's record-breaking catch.
Debutant Ben Manenti went for 23, falling to Mitch Perry who returned innings-best figures of 4-31.
With a five-way logjam at the top of the standings, victory for either side will mean a hold on top spot heading into the final round.