Aaron Mooy's second-half penalty earned City just their second win of the campaign, with the side's previous victory having also come at the expense of the reigning champions away from home in Round Five.
The result saw the Roar's brief upturn in fortunes under interim coach Frans Thijssen come to an abrupt halt, the title holders having drawn one and won one with the Dutchman at the helm following the sacking of Mike Mulvey last month.
Familiar problems remain for both sides, with City guilty of missing several chances to put the outcome beyond doubt, while Brisbane - missing star playmaker Thomas Broich as he recovers from ankle surgery - failed to mount a meaningful threat on the opposition's goal.
The winning goal came four minutes into the second half when Daniel Bowles fouled Mate Dugandzic and Mooy kept his cool from the spot.
In an indictment of the general standard at the wrong end of the table this season, City's victory takes them ahead of the Roar and into the top six, with the battle for the last finals berth thus far proving to be a race to the bottom.
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