The Tasmanians crashed to 7-45 but recovered to be bowled out for 241 on day one at Bellerive Oval, with McDermott making a gallant 128.
McDermott retired hurt on six with a lower back injury but returned for a decisive 166-run stand for the eighth wicket with Jake Doran (73). The pair were the only Tasmanians to reach double-figures.
The Tigers were in serious trouble after Victoria's 20-year-old paceman Harry Hoekstra claimed five of the initial six wickets.
Hoekstra dismissed Jordan Silk for one to start his spree, the stalwart gloving a leg-side short ball to 'keeper Liam Blackford, who completed the catch on second bite.
Fellow quick Fergus O'Neill had Teague Wylie (four) caught behind before Hoekstra snared four wickets in five overs.
The left-armer, who shone on first-class debut last-start against South Australia taking 6-103 and scoring 45 and 17, then took the wickets of Caleb Jewell (three) and Nivethan Radhakrishnan (nine), before removing Nikhil Chaudhary (five) and Mitch Owen (four) in a three-ball span.
After his first eight overs, Hoekstra had figures of 5-12. He finished with 5-46 from 20 overs.
Tasmania's fightback was expertly piloted by McDermott, whose heroics were ably supported by Doran's 208-ball knock.
McDermott accelerated late in the day in a ton laced with 13 fours and two sixes before slashing at a widish ball from Will Sutherland (1-42) to be caught at first slip, ending his 197-ball innings.
Victoria's O'Neill took 3-41 and spinner Todd Murphy 1-32.
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