Able to supplant Sydney in the top six after the Sky Blues played out a 2-2 draw with Auckland earlier on Saturday, the Reds instead collapsed to their equal heaviest defeat of the campaign at Perth's HBF Park.
Adam Taggart and Trent Ostler put the hosts ahead early, before an error from Josh Risdon teed up Ben Folami to halve the deficit in the 24th minute.
But rather than panic, the Glory steadied and kicked away in the second half via a brace from QPR-bound 18-year-old Jaylan Pearman.
Dragging themselves off the foot of the table with the victory, it was just the third win of the Glory's season and the first time they'd won a league fixture by three goals since December 2021.
Hosting Wellington before travelling to face Brisbane and Melbourne City in their remaining three fixtures, Adelaide now sit seventh, a point back of sixth-placed Sydney and a point clear of eighth-placed Macarthur, with their minus-three goal difference inferior to both.
Top of the league as recently as late January, the Reds' failure to pick up a win in two months sparked the midweek announcement that Carl Veart, in place since 2020, wouldn't return for the 2025-26 season.
Wary of disruptions, the coach had questioned the timing of the announcement and seemingly had his concerns validated when Taggart and Ostler found the net in the 11th and 19th minutes.
Risdon coughed the ball up for Folami to drag one back five minutes later but Adelaide couldn't use this as a platform, with the second half instead turning into the Pearman show.
