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The leaders snatched a 2-0 lead within 17 minutes but let their advantage slip before half-time amid a plethora of missed chances - before full-back Scott Galloway proved the hero with a masterful winner in the 73rd minute.
City opened the scoring after 14 minutes when Craig Noone slid a clever through-ball to an unchecked Connor Metcalfe, who ripped a delightful first-time strike home from a tight angle.
Three minutes later, Metcalfe released Scott Jamieson, whose squaring ball was turned into the net by Brisbane's Kai Trewin.
Noone appeared to handball in the lead-up but the goal stood.
Jamie Maclaren had a goal correctly ruled out for a handball in the 27th and, less than a minute later, Brisbane's Joey Champness cut inside and caressed a long-range shot past an outstretched Tom Glover, off the post and into the net.