The Roar could be considered fortunate to be awarded the penalty after former Manchester United midfielder Liam Miller was adjudged to have brought down Berisha in the penalty area.
Albanian Berisha, scorer of Brisbane's late equaliser, stepped up to convert the penalty in the 97th minute to complete the turnaround win and leave the majority of the 50,000 crowd at the Suncorp Stadium delighted.
The defeat was tough on Perth, who had led 1-0 with six minutes remaining but ended the game with 10-men after Dean Heffernan picked up a second yellow card shortly before Berisha's winner.
Perth owner Tony Sage was seen in tears as his players collected their runners-up medals.
"I feel like I've been robbed there with the decision, it cost us the grand final," Perth skipper Jacob Burns said of the penalty award.
"You could see plain as day... you could see it by Berisha's reaction. He came up straight up and said it wasn't a penalty. I'm just gutted."
Perth had gone in front in the 51st minute after an own goal from defender Ivan Franjoc and had looked like they would claim their first Grand Final title before Berisha headed in an equaliser with six minutes to play.
Despite the efforts of Glory goalkeeper Danny Vukovic, Berisha, the winner of this season's golden boot, came up with his 21st of the campaign at the death to claim the title.
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