After six successive home losses against the Roar, Josep Gombau's men finally broke the hoodoo in a gripping clash in front of a crowd of 20,155 to end Brisbane's season and set up a semi-final against Sydney FC.
The Reds led early through Craig Goodwin but Brisbane hit back thanks to Thomas Broich before Mabil finally settled the contest.
Though without targetman Bruce Djite, the Reds were boosted by the return from injury of the ever-dangerous Marcelo Carrusca.
But it was wingback Goodwin who set the match alight in the seventh minute when he took charge at a free-kick awarded for a foul by James Donachie on Jimmy Jego to curl a stunner from 25 metres past the desparing dive of keeper Jamie Young.
It might have been two for Goodwin in the 14th minute when he arrowed onto a pacy through ball from Sergio Cirio, but he couldn't keep his shot down.
Brisbane, with a makshift defence and only in the finals because of the expulsion of Perth Glory, found it hard to get a foothold in the match as the Reds poured forward in numbers and won possession in key areas.
Carrusca threatened in the 25th minute as he ran at the heart of the Roar defence before unleashing a 30 metre drive which dipped just over.
A calamitous mistake by defender Dylan McGowan allowed Brisbane back into the match in the 27th minute as he underhit a backpass to keeper Eugene Galekovic under presssure from Broich and the German pounced on the loose ball to steer the ball wide of the diving keeper into the far corner of the net.
Goodwin brought a fine one-handed save from Young in the dying seconds of the first half as the Reds sought to get back on top.
Pablo Sanchez should have put Adelaide back in front after being set free by Isaias in the 73rd minute, but he chipped his shot wide.
Young conjured a reflex save to deny McGowan three minutes later and then thwarted Cirio with an even better stop as the Reds turned up the heat.
The goal the Reds had been threatening finally came in the 86th minute when Cirio robbed Corey Brown and raced down the right to cut back for Mabil whose shot went in off the right hand of Young for the winner.
Gombau was rapt to progress to an away semi-final against the Sky Blues next Saturday night.
"We are happy ... we did a good game and I am satisfied with the way that the players played," Gombau said.
"In the first half we had chances to increase the score ... the second half was very equal, it was very open, and in the end we scored and went ahead."
Brisbane Roar's caretaker coach Frans Thijssen, who is expected to leave the club after its AFC Champions League campaign is concluded, lamented missed opportunities.
"We had our chances to win, we had good spells," he said.
"It's just disappointing to go out in the first round, and the way to lose the game - just before fulltime."
