City led through goals from Robbie Wielaert and Jason Hoffman, but Berisha levelled to make it 2-2 in first-half stoppage time before Victory dominated second-half proceedings in front of over 43,000 at Etihad Stadium.
The result leaves Victory top of the A League table with seven points from three matches, while City remain without a win and just two points to their name at this early stage.
City took advantage of uncertainty between Victory goalkeeper Nathan Coe and his defence in the 13th minute as Wielaert got on the end of Aaron Mooy's in-swinging free-kick from the right flank to power home the opener.
Victory were level 10 minutes later, though, Archie Thompson finishing from what may have been an offside position following good build-up play from Kosta Barbarouses and Guilherme Finkler.
Parity lasted just three minutes as Hoffman converted another pinpoint Mooy delivery as City regained the lead.
Just as it looked as though City would reach the interval with their noses in front, Berisha poached a finish after Andrew Redmayne had parried Barbarouses' initial effort.
If striker's instinct was to thank for Berisha's first, his second almost immediately after the break owed more to a slice of luck as his strike 3-2 took a deflection off Wielaert and wrong-footed Redmayne to give Victory the lead for the first time in the game.
Midway through the second half, the former Albania international completed his treble as James Brown's needless challenge in the back of Matthieu Delpierre saw referee Strebre Delovski point to the spot and Berisha did the rest, netting his second penalty in three matches to complete his first hat-trick in Victory colours.
And Thompson completed the resounding win three minutes from time, running on to an exquisite pass from Barbarouses before rounding Redmayne with ease to net his second and Victory's fifth.
