Brisbane controlled possession in the first half but looked toothless when pushing forward, however they upped the tempo after the break to blast three goals past their opponents.
The Roar's first goal came from a set piece, with Ivan Franjic launching himself at a Thomas Broich cross into the box, before a Brandon O'Neill slip gifted Liam Miller and Besart Berisha the opportunity to clumsily contrive a second, scored by the Irishman.
Broich then added a touch of genuine class to proceedings by curling in a delightful effort from long range before Perth scored a late consolation through Shane Smeltz.
Brisbane coach Mulvey admitted his side were off the boil in the opening half, but says they grew in confidence as the game progressed.
"Look, we were jittery early on," Mulvey said after the match.
"I think that was a carry on from the expectations, and last week and turning possession over a little bit too cheaply, but after that I thought we bossed possession.
"I thought we played some extremely fluid football.
"I thought that we penetrated much better in the second half than we did in the first, and that's fair, and we got three goals in the second half.
In recent weeks the ladder leaders have struggled to break down opponents who set up to defend, and Mulvey said the players had shown both patience and resolve to turn things around against Perth.
"You've got to be patient," he said.
"You saw again tonight, two banks of four, very hard to break down, narrow and compact, and when we got to one side, squeeze over.
"And it's difficult!
"When these teams come here, as they have in recent times, you need to stay focussed and concentrated and I thought that the response in the second half was really, really good.
"I'm very proud of the players and very pleased for the players because they've copped some stick of late and that's the best way to bounce back.
"We've still got a long way to go in terms of our top quality, but that was some way towards it."
