The opening stages were fiercely contested with neither side being able to create anything significant until Andrija Kaluderovic managed to get a speculative shot on goal, only to see it go harmlessly wide of the target.
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However, shortly after the midway point of the first half, Kaluderovic open the scoring after latching onto a floated through ball before firing confidently past Eugene Galekovic.
The home side should have found an immediate equaliser through either Bruce Djite or Craig Goodwin, but after both squandered close-range openings, Brisbane went two in front after Galekovic misjudged a high ball and palmed the ball into his own net.
Adelaide needed a response at the start of the second half but it took Brisbane just seven minutes to net a third. After Galekovic's clearance only found an opposition shirt, Jack Hingert played a one-two with a teammate before drilling the ball into the net.
Roar looked shell-shocked but with 19 minutes remaining, they found a way back into the game when Goodwin reacted fastest to a deep cross from the flank to direct the ball into the net from close range.
Goodwin's goal lifted Brisbane and moments later, they nearly reduced the deficit further when Djite was given time and space on the edge of the area, but the forward could only curl the ball over the crossbar.
After a late siege on the Brisbane goal, Adelaide finally netted a second in injury time when Pablo Sanchez scored from the spot after Daniel Bowles had been dismissed, but it was too little too late to prevent Brisbane recording a deserved win.