Scottish striker Hardie, signed from Plymouth Argyle for the Red Dragons' long-awaited return to English football's second tier, was on the spot to poke home from close range after being introduced as a substitute at halftime.
Hardie's goal doubled the visitors' advantage after Tom O'Connor opened the scoring for Wrexham with a neat first-half strike in front an enthusiastic crowd at Marvel Stadium.
George Evans rounded out the scoring when his long-range shot squeezed under Victory substitute goalkeeper Daniel Graskoski, and played up to the local fans with his celebration by sticking two fingers out like an AFL goal umpire.
A youthful Victory outfit was far from disgraced, with Louis D'Arrigo going closest to finding the net when his volley rattled the crossbar soon after halftime.
The friendly was a step for Championship outfit Wrexham towards their first season in England's second tier since 1982, after an unprecedented three consecutive promotions.
The club bought by Hollywood A-listers Ryan Reynolds and Rob Mac (formerly McElhenney) in 2021 will next face Sydney FC on Tuesday before completing their tour against Wellington Phoenix on July 19.
It took Wrexham midfielder Elliot Lee little more than 20 seconds to fire the first shot on target in Melbourne, but he didn't seriously trouble Victory goalkeeper Jack Duncan, who was mostly solid between the posts.
Victory's gloveman did well to tip Dan Scarr's header over the bar midway through the first half and he denied Max Cleworth's overhead kick in a similar fashion.
But Duncan's decision to punch a cross backfired in the 42nd minute when it fell to O'Connor, who fired home a first-time shot from just inside the penalty box.
At the other end, Brazilian winger Santos and Zinedine Machach both forced Wrexham goalkeeper Arthur Okonkwo into action during the first half.
Santos was substituted before the break after a heavy blow to the head from a stray pass.
Both sides made a raft of changes at halftime and Victory were almost level within one minute of the re-start through D'Arrigo's volley.
Wrexham youth product Harry Ashfield also hit the bar with a header from a James McLean cross before former Rangers man Hardie doubled the advantage from a low Ryan Barnett cross in the 66th minute.
Graskoski won't want to see a replay of Evans' goal, which he should have dealt with comfortably.
Hardie was withdrawn for the final five minutes after a knock.
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