Andy Keogh and Chris Ikonomidis both found the net as Glory moved two points clear at the top of the Hyundai A-League ladder courtesy of a hard-fought 2-0 win over Adelaide United at Coopers Stadium.
The Irishman struck on 73 minutes, the sixth time he has found the net in his last seven appearances against the Reds, while Ikonomidis bagged his second goal for the club right at the death having been teed up by former Reds man, Fabio Ferreira.
Glory's second consecutive away victory extended the club's unbeaten start to the campaign to four games, with Keogh now having scored in each of them.
In a game of few clear-cut chances played out in hot conditions in the South Australian capital, Glory's victory owed much to a solid defensive display which featured standout performances from both Shane Lowry and Alex Grant.
Head Coach Tony Popovic was understandably pleased with both the result and the performance and felt that his side were good value for the three points.
"We have to be happy,"he said.
"Coming here's not easy and they'd had a fantastic week having lifted the FFA Cup and then backed that up by with a great performance against Central Coast.
"But from the outset, I thought we were well and truly in the game, had some good opportunities and overall, got the result we deserved.
"We had a game plan to come and impose ourselves... and today it worked out.
"I'm delighted for the group that we got just rewards for an outstanding performance away from home and kept our first clean sheet against a very good opponent."
The first opening of the afternoon arrived after 12 minutes when Glory came agonisingly close to breaking the deadlock via Joel Chianese.
Keogh followed a clever turn on the halfway line by releasing the former Sydney FC man who cut in from the right before unleashing a thumping, left-foot shot which home 'keeper Paul Izzo tipped onto the crossbar.
Keogh was also involved in Glory's next chance, clipping an awkwardly-bouncing ball over the bar after more fine approach work from the lively Chianese.
But having been second-best for much of the first half, the Reds forced their way back into the contest as half time approached and thought they had won a penalty when Lowry handled Vince Lia's shot in the 41st minute.
Referee Chris Beath adjudged the incident to have occurred right on the edge of the box, however and stuck with his original decision after a lengthy referral to the VAR.
Then in first-half stoppage-time, Alex Grant produced a superb block to keep out a goalbound effort from Ryan Strain.
The home side threatened again early in the second half when Apostolos Stamatelopoulos was just unable to get enough purchase on his header after being picked out by the in-form Craig Goodwin.
Having weathered a storm of home pressure, however, Glory struck clinically at the other end.
Grant rose highest to meet Neil Kilkenny's corner and although Izzo managed to parry the defender's header, Keogh was on hand to bundle home the ball from close range.
The goalscorer was denied a second by a fine save from Izzo moments later and Glory then found themselves under more sustained pressure as the Reds threw everything at them in search of an equaliser.
Lowry produced a superb block to foil Halloran as United poured forward, but in doing so, they left themselves undermanned at the back and Glory took full advantage in the final minute of normal time.
Ferreira led a rapid breakaway and capped it by unselfishly squaring for Ikonomidis who calmly slotted home.
There was still time for Ferreira to draw another top-class block from Izzo before the curtain was brought down on a hugely-impressive away display from the men in purple.
Hyundai A-League 2018/19 Season Round 4
Adelaide United 0 Perth Glory 2 (Keogh 73', Ikonomidis 90')
Coopers Stadium, Adelaide
Referee: Chris Beath
Assistant Referee 1: Matthew Cream
Assistant Referee 2: Kearney Robinson
Fourth Official: Daniel Elder
VAR: Craig Zetter
Adelaide United: 20.Paul IZZO (Gk), 3.Scott GALLOWAY (2.Michael MARRONE 79'), 4.Ryan STRAIN, 6.Vince LIA (7.Ryan KITTO, 76''), 8.Isaías SÁNCHEZ (c), 11.Craig GOODWIN, 22.Michael JAKOBSEN, 23.Jordan ELSEY, 26.Ben HALLORAN, 31.Mirko BOLAND (10.Ken ILSØ 67'), 33.Apostolos STAMATELOPOULOS
Substitutes not used: 16.Nathan KONSTANDOPOULOS, 30.Isaac RICHARDS (Gk)
Yellow cards: Lia
Red cards: Nil
Perth Glory: 33.Liam REDDY (Gk),2.Alex GRANT, 3.Jason DAVIDSON, 4.Shane LOWRY, 5.Ivan FRANJIC, 6.Dino DJULBIC, 7.Joel CHIANESE (22.Fabio FERREIRA 78'), 9.Andy KEOGH,19.Chris IKONOMIDIS, 27.JUANDE (15.Brandon WILSON, 64'), 88.Neil KILKENNY
Substitutes not used: 1.Tando VELAPHI (Gk), 14.Chris HAROLD, 25.Walter SCOTT
Yellow cards: Kilkenny
Red cards: Nil