Perth made the trip having triumphed in just one of the previous 16 A-League meetings between the teams, while it had recorded a solitary win in its last seven outings this season.
The visitor did keep Sydney at bay during the first half, only to concede nine minutes after the break when Barbarouses's low shot from Alexander Baumjohann's through-ball slipped beyond Liam Reddy.
The manner of the goal was tough on the Glory goalkeeper, who made nine saves in total. The pick of the bunch was a low effort by his right post in the opening half, as a strong hand at full stretch made sure Bobo's header did not sneak into the net.
Sydney had 24 shots in total in the game – 16 of which came in the second half – but one goal was enough to secure the points, the victory lifting them up to fourth in the standings.