Jamie Maclaren scored his first A-League goal for Perth and goalkeeper Danny Vukovic pulled off a late save to consign Melbourne Heart to a 1-0 defeat at nib Stadium.
Perth dominated play throughout the match, but only found the back of the net once through Maclaren's 50th-minute strike.
Heart almost secured a share of the spoils at the death, but Vukovic pulled off a diving save to parry away David Williams' long-range strike.
The result left Heart winless after three rounds, while Perth moved up to sixth on the table.
Maclaren failed to play first-team football for English Championship club Blackburn Rovers during his four-year stint in England.
But the 20-year-old is hopeful a successful period with Perth will help launch his career.
Things have started well for Maclaren, who scored six goals in five pre-season games for the Glory before outpacing Heart defender Patrick Kisnorbo to score his first A-League goal.
Kisnorbo injured his leg in the process and played no further part in the match.
A crowd of 13,856 attended the match after Glory, in conjunction with Football West, gave away 5000 tickets.
Heart, missing injured skipper Harry Kewell, were forced to hang on for dear life in the opening half as Glory's Brazilian recruit Sidnei wreaked havoc on the left wing.
Sidnei rattled the post from close range in the eighth minute, and defender Scott Jamieson was also denied by the woodwork when his floating long-range strike hit the top corner.
Jamieson also had an earlier strike on goal headed away by Kisnorbo after goalkeeper Andrew Redmayne collided with another player.
But luck finally turned Glory's way in the second half, with Maclaren finding the back of the net after thumping his initial strike into Redmayne's body before drilling home the rebound.
Maltese international Michael Mifsud was starved for opportunities in his Heart debut.
Earlier, the Wellington Phoenix and Newcastle Jets remain winless after fighting out a willing but scoreless draw in Napier.
Both teams will continue to occupy positions near the foot of the table, on two points after three rounds, following the deadlock in the league's first game at McLean Park on Sunday.
It fizzled out as a spectacle following a lively first half in front of a crowd of 9020, who watched Newcastle dominate much of the opening 45 minutes but fail to capitalise.
The hosts enjoyed their best period either side of halftime, with playmaker Carlos Hernandez creating a handful of chances through testing crosses, only to be denied by goalkeeper Mark Birighitti.
It was just the third draw in 20 meetings between the teams, with the Phoenix having won 12 of their meetings and the Jets five.
Local supporters hoped the Phoenix could lodge their first win under coach Ernie Merrick but they fell short of the quality shown in last weekend's 1-1 draw away to Western Sydney Wanderers.
The Jets - like the Phoenix coming in with a first-round loss and second-round draw to their name - are still to score a goal this season.
It wasn't for lack of trying.
They produced 30 crosses to the home side's 15 and continually stretched the Phoenix in the first half courtesy of midfield dominance.
The best of several chances came in the 19th minute when a free kick from captain Ruben Zadkovich struck the crossbar. Defender Scott Neville followed up with two shots on goal from close range but was denied, firstly by goalkeeper Glen Moss and then by outstretched defender Leo Bertos.
Hernandez picked out Stein Huysegems with a perfect far-post cross minutes before the break but Birighitti produced a reaction save on the goal line.
The visiting keeper was at it again soon after halftime, keeping out a close-range stab from Phoenix captain Andrew Durante off another Hernandez curler.
Veteran forward Paul Ifill was the only Phoenix change, making his first start of the season ahead of Kenny Cunningham.
Ifill had minimal impact as his team were starved of possession and he was replaced at halftime by impressive Spanish midfielder Albert Riera.
The Jets made three starting changes from the side who drew 0-0 with Perth, introducing forward Andrew Hoole and midfielders Joshua Brillante and Ben Kantarovski for Michael Bridges, Zenon Caravella and Craig Goodwin.
Their young side - seven starting players were aged 22 or under - had too much enthusiasm for the hosts early on but they lost direction 25 minutes from the end when Zadkovich was replaced.