Roar, with Luke Brattan and Ivan Franjic scoring, set up a semi-final against Western Sydney Wanderers next Friday night.
Central Coast Mariners hosts Melbourne Victory in the other semi-final next Sunday.
Brisbane outclassed Adelaide, whose goal was scored late by Dario Vidosic, but Roar playmaker Thomas Broich and defender Jack Hingert suffered game-ending injuries.
Broich damaged his left ankle in a tackling tangle and was substituted at half-time while Hingert was subbed in the 66th minute with an twisted right ankle.
The injuries took some gloss off a sparkling triumph for Roar, with defender Brattan driving the first nail into Adelaide's coffin in the 27th minute.
Brattan snuck forward and was sighted by Broich when taking a corner and the German arrowed a long cross to his teammate.
Brattan, gifted vast space by the Reds, pulled the trigger on a low shot from 20 metres which cracked into the shins of unexpecting Adelaide defender Cassio, standing a metre from the goal line.
The ricochet gave Reds keeper Eugene Galekovic no chance and Roar took a deserved lead.
Brisbane struck a second blow one minute into injury time when Mitch Nichols created Franjic's goal.
Nichols launched a threatening cross into the box which found Franjic on an angled run, the industrious midfielder slotting a simple goal from five metres.
Roar, minus Broich then Hingert, absorbed the best Adelaide could throw at them in the second half until Reds star Vidosic scored in the 89th minute, driving home a low right-footer.But Brisbane held on against frantic Adelaide in the final minutes for a deserved victory to keep its championship defence alive.
Brisbane coach Mike Mulvey lauded his players' performance against a side who threw everything at them.
'I thought it was thoroughly deserved tonight," Mulvey said.
'To be fair, it was charge of the light brigade in the last five minutes, but we should have killed the game off before that.
'We had a couple of good chances and the game would have been over.
'The main thing is that at the end of the day the whistle has gone and we’re into the next round of the finals."