Romeo Castelen's injury meant Vidosic started for the first time in red and black, and he made his opportunity count with a superbly taken goal in the shadows of half time.
It was Wanderers first win of the season, and it dragged them off the foot of the ladder.
Perth were hit by injury, with Gyorgy Sandor, Chris Harold and Diego Castro all ruled out.
And under ever threatening dark skies at Parramatta it was the home side who were in the ascendancy.
Ante Covic received a deservedly warm reception at Pirtke Stadium, 12 months to the day when his heroics helped Wanderers win the Asian Champions League.
Why he still isn't a Wanderer remains a mystery, particularly given Western Sydney's goalkeeping stocks consist of Andrew Redmayne and Dean Bouzanis, who has suffered such a fall from grace as to go from one of the brightest young goalkeeping prospects in Europe, according to Rafa Benitez, to riding the pine at Wanderers.
Covic showed age hasn't dulled his senses with an almighty reaction save to palm a rocket from Vidosic around the near post. The save came after a miss-kick from Dino Djulbic, who was under an injury cloud after the warm up.
Dimas headed over the bar from a wicked Scott Jamieson cross, before Djulbic was lucky not to find the back of his own net when Scot Neville's cross squirmed its way into the area.
Djulbic intervened and the ball cannoned into his own cross bar.
Perth hadn't troubled Redmayne - indeed their attack was as blunt as a plastic spoon.
The heavens eventually opened, and so did Perth's defence.
A corner wasn't dealt with properly, and when Vidosic's sway of the hips earned him a yard of space, there was little doubt he would finish with aplomb. His finish flew through a crowd of players, and past Covic, in the blink of an eye.
Kenny Lowe conceded his side hadn't done enough in the first half by replacing Marc Warren, who played out of position on the left of midfield, with Guyon Fernandez.
But it was the home side who continued to dominante proceedings.
Mark Bridge, on for Jaushua Sotirio, forced another save from Covic, before Vidosic dragged a shot wide of the target.
Perth skipper Michael Thwaite was pushed forward into midfield as Lowe searched for more steel in the middle of the park, and when Wanderers lost Alberto to injury, replaced by Jonathan Aspropotamitis, Glory finally began to show themselves in the game.
Aaron Williams, brother of Australia defender Rhys, replaced the injured Diogo Ferreira, as Fernandez and Nebojsa Marinkovic began to push and probe.
Brendon Santalab made his return from various injury problens, in place of the again-ineffective Federico Piovaccari.
His wait for a goal now stretches into a fifth round, and returns of Santalab and Bridge will put him under even more pressure the longer the drought stretches on.
Wanderers began to look nervous as the match entered its final throes, but when Marinkovic curled over a free kick with only a few minutes to go, Perth's fate was sealed.
Western Sydney Wanderers 1 (Vidosic 45')
Perth Glory 0
Perth Glory 0
Pirtek Stadium, Parramatta
Referee: Matthew Conger
Crowd: 14,194
Referee: Matthew Conger
Crowd: 14,194
