Perry struck an unbeaten 58 with the bat for Victoria on Wednesday to help his side to 9-428 declared, before taking two wickets with the ball to leave the Tigers 4-201.
It came on a big day for the hosts, who had started under some pressure at 7-330 after centuries to Marcus Harris and Peter Handscomb on the opening day.
But Perry alleviated that pressure almost immediately at Junction Oval.
The left-hander combined with Ferguson O'Neill for an 83-run eighth-wicket partnership, before then helping add further runs alongside Todd Murphy.
He hit spinner Matthew Kuhnemann for a big six down the ground midway through the first session, as the morning slipped away from Tasmania.
And after the hosts declared their innings upon the fall of Murphy for 20, the quick returned to do the job with the ball.
Perry had Caleb Jewel caught behind on 32 to a ball that angled across the left-hander, before later having Jake Doran chop onto his own stumps for 33.
Pez doing it all today 😤 2 crucial wickets has Tassie 4/151 late on Day 2 — Victorian Cricket Team (@VicStateCricket) #vicsdoitbetter pic.twitter.com/sT2X2RROTiOctober 9, 2024
Ashley Chandrasinghe also took a neat catch at short leg off Murphy to discard Jake Weatherald for 28, after the opener had chewed up 101 balls in his innings.
Jordan Silk helped steady the ship late in the day for the visitors with an unbeaten 50, while Beau Webster went to stumps alongside him not out on 30.
The pair now loom as crucial in helping the Tigers avoid a big first-innings deficit, with Tasmania still trailing by 227 runs.
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