Kosta Barbarouses put the visitors ahead with a slick finish, before Eric Bautheac was dismissed for two bookable offences.
Adam Taggart then restored parity for the Roar from the penalty spot in his 100th Hyundai A-League match.
Ola Toivonen and Keisuke Honda then struck to open up a two-goal advantage, before the big Swede fired in a header at the wrong end to halve Brisbane's deficit.
Barbarouses then struck again to make it 4-2.
[Full analysis by Jeremy Eom is available on podcast.]