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Perth were denied by the woodwork down the other end inside the opening 10 minutes as Rostyn Griffiths chipped the ball over Dean Bouzanis only to see his finish kept out by the post, while Richard Garcia's rebound was saved.
The visitors continued to look the more likely as the first half progressed, and they opened the scoring when Jamie MacLaren hit a Griffiths ball forward first time, rifling the ball past Bouzanis for his ninth goal of the season.
MacLaren continued to cause problems for Western Sydney, trying to get free to receive a pass from Garcia before chipping the ball in for Danny de Silva, but neither move resulted in a goal.
Glory came close to doubling their lead just a couple of minutes into the second half as Garcia tried to head in from a free kick, nodding the ball onto the crossbar before De Silva's follow-up went high.
The hosts were back on level terms before the hour mark though as Liam Youlley forced the ball through a crowded penalty area, with the ball taking a couple of deflections before ending up in the back of the net.
Bulut unleashed a vicious strike from 25 yards out in a bid to put Western Sydney ahead for the first time, but Vuckovic watched it all the way to make the save.
Bouzanis had to remain alert between the posts for Wanderers as Perth tried to put the win beyond doubt, but the home keeper blocked a Garcia shot before claiming a MacLaren strike a couple of minutes later.
Wanderers tried to level the scores in the final five minutes when Antony Golec tried his luck from distance, but the keeper was able to tip it behind.
The result moves Perth back up to second in the table, but they can still be overtaken by Sydney FC, who are yet to play their final fixture.