In a free-flowing game which produced a cornucopia of chances, Sydney were the better side in the first half and the Wanderers finished the stronger.
Troisi was involved in both goals which came within the space of 10 minutes just after the hour.
The result extended the Wanderers' unbeaten A-League run against Sydney to five matches, their longest streak in the history of the fixture.
Wanderers' goalkeeper Daniel Margush denied Sydney strikers Barbarouses and Buhagiar with fine close-range saves inside the first four minutes.
While Sydney made most of the play in the first half, the Wanderers also created a number of opportunities.
Buhagiar was foiled again by Markush early in the second half, and the Wanderers' Nicolai Muller lobbed over the bar when clean through.
After the exchange of goals, it was the visitors who created more chances.
The Wanderers got plenty of energy and drive from young wing-backs Russell and Thomas Aquilina.
Aquilina twice went close and Troisi had a shot blocked while young substitute Patrick Wood almost scored for Sydney at the death.