After being sent in to bat, Victoria went to lunch on day one in big trouble at 4-56, with only Marcus Harris (32no off 83 balls) able to hold firm.
Pucovski survived a strong LBW shout from Harry Conway from the first ball of the innings. Three balls later he was out when he edged the paceman behind.
It was one of three catches for wicketkeeper Alex Carey during the morning session.
Peter Handscomb (10), Nic Maddinson (4) and Matt Short (5) all fell cheaply as Victoria slumped.
The damage would have been far worse if it was not for Harris, who kept his calm amid the carnage around him.
Maddinson was dropped by a diving Henry Hunt at slip, before he was out next ball edging Wes Agar behind.
Agar went to lunch with figures of 1-7 off five overs, while Jordan Buckingham (1-14 off nine overs) and Conway (1-23) also piled on the pressure.
Pucovski scored an unbeaten 193 for a Victorian second XI last month in his return from his latest concussion.
Although he was dismissed cheaply on Thursday in his first Shield hitout of the season, he will get another chance to shine in Victoria's second innings.
Pucovski's sole Test for Australia came in 2021, and he will be aiming to start the Shield season brightly in a bid to break back into the national set-up.