Hosts Perth fell behind to Marc Janko's 30th-minute penalty, awarded when Dragan Paljic pulled back Alex Brosque.
Sydney's Jacques Faty and Dino Dulbic of Perth received straight red cards six minutes later after tangling at a free-kick.
Milos Dimitrijevic added a second spot-kick for the visitors with 21 minutes remaining, only for Sydney to be reduced to nine men when Nikola Petkovic was dismissed.
Denis Kramar pulled a goal back for Perth almost immediately, yet Sydney were not to be denied and wrapped up the points courtesy of a late strike from Bernie Ibini-Isei.
Victory had earlier run out comfortable winners over Melbourne rivals City, courtesy of goals from Besart Berisha, Kosta Barbarouses and Fahid Ben Khalfallah.
Central Coast Mariners came from behind to record a surprise victory over high-flying Adelaide United 2-1 in Saturday's other match.
Nick Fitzgerald and Joshua Rose scored inside the last 11 minutes to turn things around following Awer Mabil's opener.
