Glory remain top of the Hyundai A-League table after Diego Castro's late goal secured a hard-earned 1-1 draw against Wellington Phoenix at Westpac Stadium.
Tony Popovic's men found themselves 1-0 down just before the break when Roy Krishna rifled home from just inside the box, becoming Phoenix's all-time record goalscorer in the process.
But the home side lost substitute Ryan Lowry to a red card in the 75th minute and Glory took full advantage shortly afterwards as Chris Ikonomidis delivered the low cross from the right and Castro calmly slotted home his first goal of the campaign.
The result extends Glory's unbeaten start to the season and means the WA side will head into Round 7 two points clear of second-placed Melbourne Victory.
Popovic was left to reflect upon what he described as the classic 'game of two halves'.
"In the first half, Wellington were very good and we were poor and you have to give them credit for that," he said.
"They pressed us, they moved the ball quickly and caused us problems. We seemed a little lethargic and off our game and half time couldn't come soon enough.
"But in the second half, we got into the match, we started controlling it a little better and in the end we got the goal.
"The game got more stretched in the second half and they found it hard to keep up that level of pressing as a team.
"We started to get more confident and found getting into the final third a lot easier.
"Against ten men we could have stolen it in the end, but overall, a point is good."
Phoenix began the game brightly, going close in the 10th minute when Nathan Burns dragged his shot wastefully wide having been played in by Louis Fenton and continuing to threaten once the game resumed following the lengthy delay caused by the Keogh - Kurto incident.
Liam Reddy was called upon to turn a low, 25m strike from Mandi Sosa around the post and the Glory 'keeper kept the hosts at bay again moments later when he got down well to block a snapshot from Nathan Burns.
The former Phoenix man was helpless to prevent his former club taking the lead in the shadows of half time, however, Krishna pouncing on the loose ball at the edge of the box and finding the bottom corner with a crisp strike.
Glory looked altogether brighter and more purposeful after the break and in particular, following the introduction of Castro in the 65th minute.
Moments after entering the fray, the Spaniard almost teed up Ikonomidis with some clever trickery in the box and the visitors duly began to crank up the pressure in the final quarter.
Their cause was helped by Wellington's Lowry receiving a straight red for a foul on Ikonomidis following the intervention of the VAR.
And the ten men were soon undone as Ikonomidis showed great tenacity to win the ball on the byline and cross for Castro who finished emphatically from ten metres out.
Jason Davidson was then handed the opportunity to secure a third successive away win for Glory, but he fired over after being picked out by a deep corner from Neil Kilkenny.
Hyundai A-League 2018/19 Season Round 6
Wellington Phoenix 1 (Krishna 44') Perth Glory 1 (Castro 82')
Referee: Adam Kersey
Wellington Phoenix: 1. Filip KURTO (GK) (20.Oliver SAIL (GK) 20'), 4.Mandi SOSA, 6.Dylan FOX, 8.Mitch NICHOLS, 9. Nathan BURNS (3.Reuben WAY 79'), 13. Liberato CACACE, 14. Alex RUFER (5.Ryan LOWRY 71'), 15. Michal KOPZCYNSKI, 16. Louis FENTON, 18.Sarpreet SINGH, 19.Tom DOYLE, 21.Roy KRISHNA, 22. Andrew DURANTE (C), 27. Steven TAYLOR
Substitutes not used: 11. David WILLIAMS, 23. Max BURGESS,
Yellow cards: Durante, Mandi Sosa, Cacace, Krishna
Red cards: Lowry
Perth Glory: 33.Liam REDDY (gk), 3.Jason DAVIDSON, 4.Shane LOWRY, 5.Ivan FRANJIC, 6.Dino DJULBIC (11.Brendon SANTALAB 79'), 7.Joel CHIANESE (17.Diego CASTRO 65'), 9.Andy KEOGH, 15.Brandon WILSON (20.Jake BRIMMER 57'), 16.Tomislav MRCELA, 19.Chris IKONOMIDIS, 88.Neil KILKENNY
Substitutes not used: 1.Tando VELAPHI (gk), 22.Fabio FERREIRA
Yellow cards: Ikonomidis, Lowry
Red cards: Nil