Kristian Popovic scored his first Hyundai A-League goal as Glory came from behind to secure a 1-1 draw with Western United at GMHBA Stadium.
The 18-year-old midfielder's thumping header from a Neil Kilkenny cross cancelled out Panagiotis Kone's opener for United, with both goals coming during a lively second half in Geelong.
Glory Head Coach Tony Popovic felt that given their first-half dominance in particular, his side were good value for their point.
"When you look at it, there were chances either way," he said.
"I thought we really controlled the game in the first half, but unfortunately couldn't take the lead and then they scored right at the start of the second half which gave them a real injection of energy.
"It was important that we stayed in the game in that period and Liam [Reddy} made some good saves.
"The boys that came on gave us some good energy and got us back in it.
"Kristian made a good late run [for the goal] and I'm sure it's a moment he'll remember for a long time."
Chances were at a premium in the opening 45 minutes, but the game opened up after the break and respective goalkeepers Liam Reddy and Filip Kurto were both called upon to make several crucial interventions.
Exactly as they did against Brisbane in Round One, Glory began brightly and came close to opening the scoring as early as the third minute when Kilkenny's low cross just eluded a sliding Bruno Fornaroli at the far post.
Much of the rest of the first half was characterised by the visitors enjoying the bulk of the territory and possession and penning the hosts back, though clear-cut opportunities were few and far between.
The main efforts of note both fell Glory's way, Fornaroli heading a Chris Ikonomidis cross straight at Kurto and the United 'keeper also comfortably gathering a long-range effort from Alex Grant.
The second half had barely got underway, however, when United struck with what was their first meaningful effort on target.
Connor Pain was the creator, probing away down the right and eventually laying the ball back for Kone whose fine strike from the edge of the box found the top corner of Reddy's net.
The Glory 'keeper then did superbly to prevent the hosts from doubling their lead when he somehow managed to tip a fierce strike from Alessandro Diamianti around the post.
At the other end, meanwhile, a short corner routine ended with Ikonomidis firing wide and moments later, Gregory Wuthrich's deep cross was met by Kim whose firm header drew a reflex save from Kurto.
The home 'keeper was helpless to prevent Glory from restoring parity 14 minutes from time, however, Kristian Popovic timing his run perfectly to meet a sublime Kilkenny cross and power his header into the net.
That goal prompted a frantic finale in which Kurto was forced into a smart save to keep out Fornaroli's stinging strike and Reddy then responded in kind to deny Kone low to his right.
United substitute Dylan Pierias was next to go close, rattling the crossbar having been sent clear down the right, before Chris Harold went close for Glory and Diamanti was centimetres away from restoring the home side's lead as the goalmouth continued right up to the final whistle.
Western United 1 (Kone 48') Perth Glory 1 (K.Popovic 76')
GMHBA Stadium, Geelong
Referee: Alireza Faghani
Assistant Referee 1: Matthew Cream
Assistant Referee 2: Andrew Meimarakis
Fourth Official: Alex King
VAR: Kris Griffiths-Jones
Western United FC: 1.Filip KURTO (gk), 4.Andrew DURANTE, 6.Connor CHAPMAN, 8.Panagiotis KONE, 10.Scott McDONALD (14.Max BURGESS 79'), 11.Connor PAIN, 12.Dario JERTEC, 18.Besart BERISHA (5.Dylan PIERIAS 83'), 19.Joshua RISDON, 22.Ersan GULUM, 23.Alessandro DIAMANTI (c)
Substitutes not used: 2.Aaron CALVER, 15.Jonathan ASPROPOTAMITIS, 20.James DELIANOV (gk), 26.Kwabena Appiah-Kubi, 27.Jerry SKOTADIS
Yellow Cards: Jertec 38', Kone
Red Cards: None
Perth Glory: 33.Liam REDDY (gk), 2.Alex GRANT, 4.Gregory WUTHRICH, 7.Joel CHIANESE (3.Jacob TRATT 68'), 9.Bruno FORNAROLI, 12.Kim SOO-BEOM 13.Osama MALIK, 17.Diego CASTRO (c), 19.Chris IKONOMIDIS, (14.Chris HAROLD 76'), 27.JUANDE (29.Kristian POPOVIC 68'), 88.Neil KILKENNY
Substitutes not used: 1.Tando VELAPHI (gk), 6.Dino DJULBIC, 28.Gabriel POPOVIC
Yellow Cards: Grant
Red Cards: None