Three runs behind the required run-rate on the final ball of the 29th over, Victoria middle-order batsman Matt Short struck Jason Sangha over long on for six with the umpires immediately taking the players from the field due to bad light at Junction Oval.
The unlikely finish overshadowed Daniel Hughes's earlier heroics with the NSW opener striking an impressive 117 and extending his record of most one-day centuries for the Blues to eight.
In pursuit of NSW's challenging 7-277, Victoria reached 0-47 from 9.2 overs when a 13-over delay saw the home side set a revised target of 226 from 37 overs at just over a run-a-ball.
Pucovski played a chanceless innings of 64 before he fell to a sharp catch behind the stumps from new wicketkeeper Matthew Gilkes off the bowling of Liam Hatcher.
Test opener Marcus Harris, batting at No.3, fell in the next over for 41 to leave Victoria - missing the services of quick-scoring Nic Maddinson due to English County commitments - significantly behind the required run rate.
But Short (17 not out) and captain Peter Handscomb (11 not out) edged Victoria to 3-158 and over the line without any room to spare.
NSW seemed on top throughout the day as Hughes took early control after the visitors were given first use of the deck.
Hughes enjoyed strong support from fellow opener Kurtis Patterson (30), Moises Henriques (35) and Matthew Gilkes (40).
In his 88th appearance, Henriques broke the record for most one-day appearances for NSW.
Hughes looked capable of a massive score but a remarkable grab behind the stumps from stand-in wicketkeeper Handscomb ended his knock in the 43rd over.
A slew of late wickets marginally slowed the Blues scoring with debutant allrounder Will Salzmann contributing a whirlwind 21 not out from 14 balls in the final overs.
Inexperienced left-arm spinner Todd Murphy continued where he left off last season with a tidy 10-over return of 2-29.
