Two goals in the final four minutes from former Glory midfielder Jake Brimmer consigned Richard Garcia's men to a 2-1 defeat against Melbourne Victory at AAMI Park.
The WA side had looked on course to claim a second victory of the season when Bruno Fornaroli nodded home Carlo Armiento's fine cross in the 62nd minute.
But Brimmer headed the navy-and-whites level four minutes from the end and then sealed the deal from the penalty spot after substitute Josh Rawlins had handled the ball in the area.
Glory had earlier been grateful to Tando Velaphi who marked his first start of the season by making several fine saves from Marco Rojas, but the visitors also went close themselves through Fornaroli and Armiento.
In his post-match media conference, Garcia suggested that fatigue and inexperience had been major contributors to his side's defeat.
"We're getting better at backing up, which is fantastic," he said, "but it's always hard when you have to play three games in six days and there were a few tired bodies out there.
"When you're coming into the late stages and you're bringing young boys off the bench that don't have that experience, sometimes you cop goals.
"It's a tough schedule for us - we've been asked to play four games in 12 days which is pretty tough, I think, for anybody.
"We're probably the only people that are being asked to do that, but that's what happens and we've got to deal with it.
"We started slow against Western United and again tonight you could see the guys that have played most of the minutes looked fatigued in the first half and it took them quite a while to get up to speed."
The men in white showed plenty of attacking intent right from the off, with Ryan Shotton and Leigh Broxham both forced into some desperate defending to keep the home goal intact.
The home side's response was led by the lively Rojas who drew the game's first save from Velaphi after weaving his way into the box and unleashing a low shot.
And Victory threatened again moments later, Robbie Kruse cleverly teeing up Brandon Lauton who clipped his shot across the face of the goal and wide of Velaphi's left post.
Brimmer was the next to go close, forcing Velaphi to palm his well-struck effort against the post, but Glory replied within seconds by carving out a decent opportunity for Fornaroli who was kept at bay by a smart, one-handed save from Max Crocombe.
As the chances continued to flow, Velaphi reacted superbly once again in the 34th minute, this time to foil Rojas after the Kiwi forward had met an Adama Traore cross with a powerful, first-time strike.
Within three minutes of the restart, the Glory 'keeper continued his duel with Rojas, producing a spectacular, one-handed save to block the Victory man's dipping shot from just outside the box.
Crocombe responded in kind soon after, reacting quickly to keep out a cross-shot from the in-form Armiento.
Undeterred, Armiento continued to trouble the Victory defence and it was the 21-year-old who played a key role in Glory breaking the deadlock just after the hour-mark, whipping in a delightful cross which was clinically converted by Fornaroli.
Stung by that setback, the hosts threw men forward and came close to levelling things up in the 67th minute as Kruse got away down the right and drove in a low shot which flashed centimetres wide of the far post.
They finally got their reward four minutes from time when Traore picked out Brimmer in the box and the midfielder's header found the bottom corner of Velaphi's net.
And in a painful denouement for the visitors, Brimmer snatched all three points for his new club, calmly firing home from the spot after Rawlins' indiscretion in the box.
Melbourne Victory 2 (Brimmer 86', 89' (pen)) Perth Glory 1 (Fornaroli 62')
AAMI Park, Melbourne
Referee: Shaun Evans
Melbourne Victory: 20.Max CROCOMBE (gk), 2.Storm ROUX, 3.Adama TRAORE, 5.Ryan SHOTTON, 6.Leigh BROXHAM (c) (13.Birkan KIRDAR 78'), 8.Jacob BUTTERFIELD, 10.Robbie KRUSE (25.Luis LAWRIE-LATTANZIO 78'), 16.Brandon LAUTON (17.Elvis KAMSOBA 46'), 19.Dylan RYAN, 22.Jacob BRIMMER, 23.Marco ROJAS (V 90+3')
Substitutes not used: 1.Matt ACTON (gk), 15.Aaron ANDERSON, 35.Zaydan BELLO
Yellow Cards: Shotton
Red Cards: None
Perth Glory: 1.Tando VELAPHI (gk), 9.Bruno FORNAROLI, 10.Andy KEOGH (21.Bryce BAFFORD 79'), 15.Brandon WILSON (19.Calllum TIMMINS 72'), 16.Nick SULLIVAN (22.Josh RAWLINS 64'), 18.Nick D'AGOSTINO (24.Daniel STYNES 63'), 20.Carlo ARMIENTO, 23.Dane INGHAM, 29.Darryl LACHMAN, 37.Riley WARLAND, 88.Neil KILKENNY (C)
Substitutes not used: 5.Jonathan ASPROPOTAMITIS, 33.Liam REDDY (GK), 34.Mason TATAFU
Yellow Cards: Armiento
Red Cards: None