© Getty Images
Sydney responded when Brosque lined up an effort from 25 yards when he was afforded space and time on the edge of the box, but his effort was saved by Mark Birighitti.
The Jets thought that they had taken the lead when Jason Hoffman rose highest at the back post to head home a free kick, but the goal was chalked off for offside.
The visitors threatened before the break when Brosque and Milos Ninkovic combined to tee up Rhyan Grant on the edge of the area, but his strike was well saved by Birighitti.
Sydney upped the ante late in the game and came close to going ahead as George Blackwood released the run of Shane Smeltz through on goal, and the forward lifted his effort over substitute keeper Ben Kennedy, only to see the ball drop over the bar.
The away side came closer still when Brosque collected the ball and raided inside the box, but his strike clattered off the post and bounced clear.
Sydney finally got their winner in the 89th minute as Alex Gersbach lifted the ball in from the right and Brosque beat his man at the near post to send an effort beyond the reach of Kennedy.