Victory striker Besart Berisha made up for his first-half penalty miss with a successful spot kick in the 58th minute.
But the Glory stormed back into the contest, with Nebojsa Marinkovic nailing a 21m free kick in the 71st minute, before Adam Taggart scored the winner with an 84th-minute tap-in.
The win keeps the fifth-placed Glory in touch with the top four.
Victory, who lost 3-0 on Tuesday to Wellington, are eight points adrift of ladder leaders Sydney FC ahead of their January 26 showdown in Melbourne.
The Glory are on a five-match unbeaten run, but it's not all good news at the club.
The farce surrounding Glory defender Rhys Williams took another bitter turn when the former Socceroo ruled himself out of playing.
Williams, who had been left out for five straight games after requesting a transfer from the club, was named in the extended squad for the Victory clash.
With Rostyn Griffiths (suspended), Alex Grant (foot) and Chris Harold (shoulder) all absent, Williams loomed as a key inclusion for the Glory.
But the 28-year-old didn't train on Friday after complaining of a hamstring injury, ruling him out of the match.
Glory chief executive Peter Filopoulos took to Twitter that night to take a subtle swipe at the star recruit.
"Rhys Williams did not train tonight due to reported hamstring injury. Good news is MRI and ultrasound have shown all clear," Filopoulos wrote, before adding: "You can lead a horse to water but you can't make it drink."
Victory coach Kevin Muscat made five changes to his starting XI following shock away loss to the Phoenix.
Fahid Ben Khalfallah and Jason Geria were suspended, while star midfielder Marco Rojas was given a well-earned rest on the bench.
Nick Ansell and Oliver Bozanic were left out of the squad following the club's hectic travel schedule, and the new-look side struggled to create opportunities in the first half against Perth.
Victory were awarded a penalty in the 44th minute when Glory defender Shane Lowry lost his footing and brought down James Troisi.
Berisha stepped up to take the penalty, but goalkeeper Liam Reddy pulled off a stunning save to his right.
It continued Reddy's hot form this season, with the 35-year-old also saving two penalties in the Glory's 3-3 draw last month with Melbourne City.
But Berisha was given the chance to atone when Glory defender Joseph Mills brought down Troisi in the 57th minute.
Marinkovic levelled the scores when he curled his free kick around the Victory wall.
And a superb run down the right from Josh Risdon set Taggart up for the winner in front of 11,271 fans.
