Juan Muniz and Jonny Yull both found the net in the first half on Friday night before a sublime team goal finished by Luka Jovanovic almost immediately after the restart ensured victory for the home side.
Substitute Luke Duzel iced the win in added time with a stunning solo effort.
The win was the second on the trot for United who climbed to third on the table, level on 29 points with second-placed Auckland FC.
United coach Airton Andrioli was delighted with his team's display. "Very pleasing with the way we started the game, the way we managed the game and the way we finished the game, so it was a very good performance," he said.
The Reds broke the deadlock on 12 minutes with a well-taken set piece from Muniz after Ethan Alagich was fouled on the edge of the area.
The Spanish No.10 stepped and whipped his shot into the far corner. Glory shot stopper Matt Sutton got his hand to the strike but couldn't keep it out.
Perth found chances hard to come by, but full-back Charbel Shamoon did give United a scare when his trivela went just wide of Joshua Smits' post on 26 minutes.
Adelaide doubled their lead three minutes later after the Glory coughed up possession in defence.
Ryan White pounced and slipped through Jovanovic who blasted a shot at goal from 15 metres. Sutton managed to save that effort but the rebound sat up perfectly for Yull who volleyed first time from the edge of the area.
The home side began the second half exactly how the finished the first, finding the back of the net within three minutes of the restart.
The Reds completely dismantled Perth, going coast-to-coast and leaving the visitors chasing shadows.
Alagich won the ball deep in the defence, exchanged passes with Jovanovic before releasing White who in turn laid off to Yaya Dukuly.
The Reds speedster charged towards goal before threading a pass for White, before squaring for Jovanovic who tapped into an empty net.
On 78 minutes, the Glory's Andriano Lebib was shown a red card after high contact with Adelaide substitute Brody Burkitt.
After referee Shaun Evans was called over by VAR, the expulsion was reviewed and eventually overturned.
Just as regulation time ticked over, substitute Luke Duzel capped Adelaide's stellar performance with a brilliant solo goal.
He skipped past and danced through three defenders before firing home past Sutton, who again managed to get a glove to the ball but couldn't keep it out.
Glory coach Adam Griffiths said Perth's performance was well below par.
"It wasn't good enough. We had a good turn-out of supporters, Perth Glory fans turning up for us, and that was not good enough."
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