Ivan Franjic broke the deadlock in the 57th minute when he headed home a Thomas Broich free-kick, before goals from Liam Miller and Broich sealed the result for the Roar.
Shane Smeltz scored a late consolation for the Glory but the visiting side were no match for a rampant Brisbane for the majority of the second half.
Despite plenty of possession, the Roar looked toothless going forward early on, but upped the tempo as the match wore on before eventually killing off their opponents.
Perth came out with all guns blazing, creating a host of chances in the opening five minutes.
A double blunder by Franjic enabled Sidnei to advance on the Roar goal from the left, but his shot was deflected past the near post.
From the resulting corner, Brandon O'Neill was given too much space but could not hit the target with his close range header.
Moments later Sidnei was again left to his own devices down the left, and this time it took a brilliant save from Michael Theo to deny the Brazilian a goal.
Brisbane dominated possession but, as has been the case in recent weeks, struggled to convert that dominance into chances.
Besart Berisha was fouled on the edge of the box to earn a dangerous free kick for the hosts in the 22nd minute, but Dimitri Petratos fired the chance just over the crossbar.
The Roar persisted with attacks down the right through Franjic and Petratos until a quick transition to the left almost produced a goal, as Broich sent a low pass right across the face of goal that only required some kind of touch to end up in the back of the net.
It took until after half time for Brisbane to really trouble Perth goalkeeper Danny Vukovic, who was forced to palm away a searing Matt McKay shot from wide on the left in the 48th minute.
Broich then found enough space for a shot, which may have been heading wide but was nevertheless blocked by the head of O'Neill.
Brisbane's increased vigour in the second term eventually paid dividends when Broich curled in a free-kick from wide on the right and a flying Franjic headed it home at the back post.
Perth defender Jack Clisby made a desperate slide to deflect a Petratos shot wide, after the forward had been put through on goal by Brattan, as the game opened up for the Roar.
A well-executed Brisbane counter attack almost resulted in a second goal as Berisha fed Petratos who cut inside with some nifty footwork before firing his attempt over the bar.
A Broich effort from outside the box ricocheted to the feet of a lurking Berisha to give him a one-on-one chance against Vukovic, but the Perth keeper somehow got a foot to the Albanian's low shot.
Berisha and Miller then did their best to bomb an outrageously easy chance when O'Neill lost possession to send them through against a stranded Vukovic.
The two Roar players almost had too much time on their hands to concoct a way to beat the keeper, exchanging passes before Miller had a shot blocked then managed to finally bury the rebound.
Four minutes later Broich sealed the deal with a sumptuous curled effort from just outside the area that sailed into the top corner.
Perth did manage to find a consolation goal after a terrible error from Brisbane captain Matt Smith, who played a ball across his own goal straight into the path of Smeltz, who finished past Theo.
