Mike Mulvey's side came in to the clash at the Suncorp Stadium having taken just one point from their last three top-flight fixtures, and went in at half-time drawing 0-0 with the struggling Glory.
However, a second-half blitz secured the hosts' win, which moves them seven points clear of Western Sydney Wanderers at the top of the table.
Ivan Franjic broke the deadlock on 57 minutes, and former Celtic and Manchester United midfielder Liam Miller all but secured the points with 10 minutes remaining.
German Thomas Broich made it 3-0 in the 90th minute, before Shane Smeltz grabbed an injury-time consolation for Perth.
The Glory, who slip bottom of the table on goal difference as a result of their defeat, began the game on the front foot and created a host of chances in the opening five minutes.
Brisbane dominated possession, but struggled to make this count in front of goal before Franjic nodded them in front shortly before the hour mark.
Miller and Broich then calmed the nerves of the home side, whose only negative point of the game came in the closing stages when a defensive error from skipper Matt Smith enabled Smeltz to ruin their clean sheet.
