Marco Rojas scored twice in the 23rd and 73rd minutes, sandwiching a goal from Archie Thompson (67), as the home side took control of proceedings.
Sydney's cause was not helped by a red card for Tiago on the hour mark, and although Joel Griffiths got them on the scoreboard 15 minutes from time, Fabio Alves was also sent off late on to cap a frustrating evening.
Victory lie five points behind leaders Central Coast Mariners and one ahead of Western Sydney Wanderers, who edged out Melbourne Heart 1-0.
The home side had to play most of the match with 10 men following the 14th-minute dismissal of Jerome Polenz, but Shinji Ono's penalty after 73 minutes was enough to secure the points.
In Saturday's other match, Brisbane Roar moved four points clear of the foot of the table with a 1-0 win at Perth Glory, courtesy of James Meyer's 17th-minute strike.