Tasmania, who won the toss and elected to bat, reached 5-250 at stumps on day one at Melbourne's Junction Oval.
McDermott was dismissed in the final over of the day, caught in the slips off the bowling of Will Sutherland for 94.
McDermott hit nine boundaries and two sixes in a largely faultless 209-ball knock.
McDermott's 129-run stand for the third wicket with former Vic Matthew Wade was the main plank in Tasmania's innings, with the pair batting throughout the afternoon session.
Former Test batter Wade looked at ease during his 61 from 129 balls, before feathering a catch to the wicketkeeper off the bowling of rookie spinner Todd Murphy.
Playing in just his second Shield match, the 21-year-old offspinner made a double breakthrough earlier in the day after the Victorian quicks failed to make inroads.
Murphy (3-58 off 23 overs) delivered successive wicket-maidens as openers Caleb Jewell (27) and Tim Ward (29) were dispatched.
Jordan Silk hit six boundaries in his 31 before becoming another victim of spin as Jon Holland got into the action.
It was a costly final half-hour for the Tigers who lost 2-4 in the dying stages.
Jake Doran (2no) and Tom Rogers (0no) are currently at the crease.
It was a different-looking Victoria side from the one who drew against Queensland last month with James Seymour, Jake Fraser-McGurk and Henry Thornton all coming into the line-up.
Opener Marcus Harris and fast bowler Scott Boland are in Pakistan with the Australian Test squad, while Matt Short has a side strain.
Concussion victim Will Pucovski is continuing his return to cricket with a Victorian Second XI match this week.
Unbeaten Victoria currently sit second on a congested Shield ladder with two wins and three draws, with Tasmania also boasting two wins.
