Victory went into Sunday's clash at AAMI Park on a high from winning their opening two games of the season, but they were brought back down to earth by Perth.
Rai Marchan was shown a straight red card for catching Bruno Fornaroli with a high boot following a VAR check and Glory capitalised to claim their first win of the campaign.
New signing Burke-Gilroy opened the scoring with a sweet left-foot strike from outside the penalty area after 66 minutes, before whipping in a cross for Ciaran Bramwell to nod beyond Ivan Kelava.
Captain Fornaroli rifled in a third with his right foot from 20 yards out in the closing stages as Perth ended a run of six matches without an A-League win.
Macarthur rose to the summit courtesy of an own goal from Central Coast Mariners captain Oliver Bozanic on the stroke of half-time.
Ulises Davila's strike deflected off Bozanic and in for the only goal of the game to give Macarthur a first regular-season win over the Mariners at Panthers Stadium, where Central Coast goalkeeper Yaren Sozer was forced off with a suspected torn hamstring.