A week after it was announced coach Tony Popovic was leaving the club, the Wanderers scored twice late in the first half to secure a win for caretaker coach Hayden Foxe.
He had some nervous moments, as Perth created several chances in the last half hour and scored in the 82nd minute.
With new recruits Alvaro Cejudo, Oriol Riera and Roly Bonevacia prominent, Wanderers played some neat, attractive football and should have had the match wrapped up inside the first hour.
They had to wait 43 minutes for a goal, with Spanish striker Riera pouncing on a through ball from compatriot Cejudo and driving the ball past Glory goalkeeper Liam Reddy.
Japan's Jumpei Kusukami was equally clinical in the one minute of added time when he was released by Brendan Hamill.
The Wanderers could have doubled their lead within seven minutes of the second half, but couldn't capitalise on two close-range chances.
Cejudo had a shot blocked by Reddy and Riera lifted the ball over the bar after being put through by Chris Herd.
Perth surged back into the game, with striker Adam Taggart hitting the post and crossbar in the space of two minutes and Wanderers goalkeeper Vedran Janjetovic making a number of saves.
They finally got on the scoreboard when an header from skipper Andy Keogh deflected off Hamill and into the net.