Archie Thompson's 94th-minute goal - a header from a Marco Rojas cross - swung a drama-charged eliminator Victory's way after luckless Glory had imploded late on in a tale of two penalties.
First Shane Smeltz wasted one for Glory two minutes from the end of normal time for what would have been an unassailable 2-0 lead.
Then at the other end, a controversial 90th minute call from referee Jarred Gillett - the man who angered Glory in last season's grand final loss to Brisbane with a late penalty decision - made another contentious intervention.
This time, he missed a handball by substitute Andew Nabbout before ruling he had been fouled by Steve Pantelidis, who was also sent off before Mark Milligan fired Victory level just to compound Glory's misery.
Alistair Edwards' men, who sneaked into the play-offs in sixth spot, looked on course for a grand final qualifier against Premiers' Plate winner Western Sydey Wanderers next Friday at Parramatta Stadium thanks to a first half goal for Japanese ace Ryo Nagai. Now it will be Victory facing Central Coast next Sunday.
The game turned on its head in the dramatic dying embers of normal time when Smeltz missed an 88th minute penalty after Milligan had felled Scott Jamieson, his shot cannoning back off the crossbar.
And before the crowd could draw breath Gillett had pointed to the spot at the other end.
This time Pantelidis was the villain, allowing Milligan to make up for his faux pas at the other end and guide home his ninth goal of the season.
Glory was rewarded for a bright start when loan striker Nagai scored his second - and most crucial - goal for the club to give the visitor a surprise 14th-minute lead.
In-form left-back Jamieson was the architect, his beautifully flighted cross evading the flapping fingers of Victory goalkeeper Nathan Coe and falling into the path of 20-year-old Nagai, who improvised to cleverly chested the ball into an unguarded goal.
It was no more than Glory deserved as it took the game to the home side early on as it sought just its fourth road win of the campaign.
A relieved Thompson admitted Glory was desperately unfortunate not to still be alive in the finals.
"They put in a great performance, the best I have seen them this season and we got a bit lucky," he said.
"We never gave up and are delighted to have come from behind to win, but you can't take it away from Perth. They gave us a lot of problems and will feel hard done by."
Victory was slow to respond to Glory's opener and it wasn't until the 34th minute that it carved out its first meaningful chance - midfieldier Leigh Broxham firing wide after being set free inside the box by the elusive Rojas.
Victory coach Ange Postecoglou sent on the creative Marcos Flores early in the second half as he hunted a spark of invention to unlock Glory.
But it was Glory which could have killed off the contest on 57 minutes when Smeltz - who had 14 stitches removed during the week - found himself one-on-one with Coe but took too long before uloading and ultimately fired wide via Coe's out-stretched fingers.
At the other end Flores had an immediate impact, flashing a header just over.
The drama continued in extra time with Glory - despite having a man fewer - dominating and having another call for a spot kick denied when Nagai went down.
Rojas and Nabbout missed sitters in the final minutes as brave Glory ran out of legs.