Glory remain unbeaten in the Westfield W-League this season after a brace from Sam Kerr helped secure a battling 2-2 draw against Adelaide United at the Marden Sports Complex.
The Matildas star struck twice in the final moments of the first half to cancel out Veronica Latsko's opener for the hosts and send the visitors into the break 2-1 up.
But Glory's night took a dark turn in the 58th minute when Alyssa Mautz was sent off and Latsko duly bagged her second of the game to secure a share of the spoils for Ivan Karlovic's side who also remain unbeaten this term.
Kerr's double takes her tally for the season to six and remarkably, means that she has now scored eight times in her last seven appearances against the South Australians.
Mautz, meanwhile, became the second Glory player to be sent off this season after Sarah Carroll was dismissed, also by referee Katie Patterson, in the away draw at Canberra.
Despotovski was incensed by the decision which saw his side forced to play out the last half-hour with ten players, but felt that his charges could still have emerged with three points.
"We didn't play the best, but I think we did enough to win the game,"he said.
"It wasn't to be because of certain circumstances, that I cannot talk about, which now mean we will miss one of our key players next week through suspension.
"We worked hard in hot conditions to get back into the game after the long ball caught us out for their opening goal and then in the second half we started a bit sluggishly but got back into the game.
"It's disappointing that we then conceded from a corner and these are things that we have to address because they are not one-offs.
"But we'll take the point, regroup and prepare for Newcastle next week. What's most disappointing is not so much that we've dropped two points depending on how you view the game, but that we will lose a very important player for our next game."
Glory came close to hitting the front inside the first minute when Hill was played in by Kerr only to be denied by a fine sprawling save from the alert Sarah Willacy.
Kerr then fired straight at the Reds' 'keeper after being played in by Shannon May as the visitors continued to look the more likely and yet it was the hosts who hit the front on 22 minutes.
Latsko showed great strength to hold off Katie Naughton on the edge of the box before rifling home a shot which gave Eliza Campbell no chance.
The goal briefly knocked Glory out of their stride, but they steadily regained the ascendancy as half time approached and changed the whole complexion of the game with two quickfire goals.
The first came when Kerr rose highest to meet Mautz's deep cross from the right and the Matildas star grabbed hers and Glory's second seven minutes later after being picked out by a raking cross-field ball from Hill.
The proceedings took another dramatic twist just short of the hour-mark when Mautz received a second yellow card after an innocuous tangle with Laura Johns and from the resulting free-kick, Gunnhildur Jonsdottir somehow managed to knee the ball onto the crossbar with the goal at her mercy.
Continuing to exploit their numerical advantage, Adelaide piled the pressure on during the final quarter and eventually drew level 11 minutes from time.
Laura Johns delivered the corner and after Jonsdottir struck the woodwork for the second time in the game, Latsko was on hand to slam home the loose ball.
To their credit, Glory dug deep in the final moments of a compelling contest and were denied a likely late winner when Willacy pulled off a superb save to block Kerr's stinging drive.
Westfield W-League 2018/19 Season Round 6
Adelaide United 2 (Latsko 22', 79') Perth Glory 2 (Kerr 40', 45+2)
Marden Sports Complex
Referee: Katie Patterson
Assistant Referee 1: Isabella Blaess
Assistant Referee 2: Paula Orlandi
Fourth Official: Jack Robinson
Adelaide United: 1.Sarah WILLACY(gk), 2.Emily HODGSON, 5.Gunnhildur JONSDOTTIR, 8.Emily CONDON (3.Charlotte GRANT 78'), 9.Fanndis FRIDRIKSDOTTIR (7.Isabel HODGSON 46'), 11.Laura JOHNS, 12.Veronica LATSKO, 15.Emma CHECKER (c), 16.Dylan HOLMES, 22.Amber BROOKS, 23.Michelle HEYMAN
Substitutes not used: 6.Georgia CAMPAGNALE, 20.Sian McLAREN (gk)
Yellow cards: Holmes
Red cards: Nil
Perth Glory: 1.Eliza CAMPBELL (gk), 3.Kim CARROLL, 4.Alyssa MAUTZ, 5.Shannon MAY, 7.Nicole STANTON , 9.Rachel HILL, 11.Leticia MCKENNA (6.Abbey MEAKINS 59') , 12.Jenna ONIONS, 20.Sam KERR (c), 24.Natasha RIGBY, 25.Katie NAUGHTON
Substitutes not used: 13.Jamie-Lee GALE , 22.Abbey GREEN, 23.Stacey CAVILL (gk)
Yellow cards: Rigby, Mautz, Meakins
Red cards: Mautz