City dictated the early passages of play, but it was Sydney's Marc Janko who came closest to opening the scoring.
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The forward found space in the box and unleashed a shot at goal, and although his effort passed the goalkeeper, the ball was denied by the post.
Sydney began to take control of the game, but while they had the majority of possession, they struggled to create any meaningful chances at goal.
Towards the end of the first half, the Sydney players called for a penalty when Janko was brought down by Patrick Kisnorbo in the area, but the referee wrongfully waved it away.
Just minutes before the half came to an end, the visitors came inches away from scoring against the run of play when Jonatan Germano fired a shot at goal, but goalkeeper Vedran Janjetovic tipped the ball over the bar.
After the break, City had an early chance when Germano cut the ball back to Mate Dugandzic in the box, but the forward failed to get his shot away.
The contest opened up as the second half went on and Bernie Ibini-Isei came close when his shot clattered off the post, leaving Janko frustrated as he was waiting unmarked on the right.
The deadlock was eventually broken when Brown stormed into the box and got around the keeper before slotting the ball into the back of the net, which is his first A-League strike in three years.
City are now in sixth place on 28 points.