Des Buckingham's side was 2-0 up after only 17 minutes, Connor Metcalfe blasting past goalkeeper Jamie Young before Scott Jamieson doubled the lead via Brisbane's Kai Trewin.
The visitor, which felt a handball should have been given against Craig Noone in the build-up, responded impressively to draw level before half-time through a fine Joey Champness strike and a Macaulay Gillesphey header.
City, which fired in 33 shots across the 90 minutes, failed to capitalise on its chances until some brilliance from Scott Galloway, the full-back's superb run sending him into the box where he hooked a clever finish into the left-hand corner after his cross had been blocked.
City is nine points clear of the chasing pack, with Sydney FC, Adelaide United, Central Coast Mariners and Macarthur all on 32 points.
In the later match, Perth Glory beat Melbourne Victory 2-1 at HBF Park to move seven points clear of the bottom two and keep its top-six hopes alive.
Robbie Kruse missed a first-half penalty for the visitor, which was given an uphill task when Nicholas Ansell was sent off 48 minutes in for a crude challenge on Callum Timmins.
Diego Castro combined well with Ciaran Bramwell to set up Bruno Fornaroli to open the scoring, with Chris Ikonomidis volleying home the second. Rudy Gestede grabbed a consolation for Victory after Kruse hit the crossbar.
Perth is nine points adrift of Western Sydney Wanderers in sixth but has two games in hand.