A week after his brilliant individual effort sealed all three points late on at home to Sydney FC, David Williams was the match-winner again for Heart.
The 25-year-old forward came off the bench to net the decisive goal and make it an improbable three wins from four attempts for the previously hapless team in red and white, who are now unbeaten since losing away to the Glory on January 10.
Williams' 12th strike for the club also saw him become the joint leading goal-scorer in Heart's brief A-League history, an accolade he shares with Eli Babalj.
Defender Patrick Kisnorbo had given Heart the lead five minutes into the second half. Steven McGarry equalised for the Glory with 17 minutes to go, before Williams intervened to see John van 't Schip's resurgent side close to within eight points of a finals berth.
Wellington Phoenix occupy sixth spot following their victory away to the Newcastle Jets on Sunday afternoon, and it is the New Zealand side who are up next for Heart at Westpac Stadium in Round 19.
There were fresh faces in the line-up for both teams, as Stefan Mauk and Darvydas Sernas made their first starts for Heart and Glory respectively, while former Central Coast Mariner Rostyn Griffiths debuted for Perth.
The wisdom of playing a football match in 40-degree heat at the Lavington Sports Grounds was the subject of much discussion leading up to Sunday.
And although Football Federation Australia opted early on the morning of the game to push kick-off back by two hours to 5pm, the searing conditions in regional New South Wales contributed to a sluggish start.
It took until the seventh minute for Harry Kewell to threaten the Glory goal with a half-chance, and it was another 17 minutes before either keeper was genuinely called into action, when Perth's Danny Vukovic had to tip over a fierce Iain Ramsay drive.
Jonatan Germano poked a weak effort straight at Vukovic from the resulting corner, before Jason Hoffman and Mauk both headed presentable chances straight at the Glory custodian shortly before half-time.
The away side meanwhile were restricted to a hopeful penalty appeal when Robbie Wielaert brought down Chris Harold on the edge of the penalty area, while Jacob Burns fired over the bar from a Shane Smeltz cut-back in first-half injury time.
Heart certainly showed more initiative in the opening 45 minutes, and they received a belated reward early in the second period, when Kisnorbo rose above McGarry to head home the opening goal from Ramsay's corner.
Perth's recent arrivals understandably wilted relatively early, with Lithuanian Sernas replaced by Sidnei Sciola and Griffiths making way for another new signing, Nebojsa Marinkovic, on 65 minutes.
Heart made changes of their own, with Kewell and Mauk replaced by Ben Garuccio and David Williams respectively before the hour mark.
It was the Glory however who benefitted from shaking things up. In the 72nd minute Smeltz saw a header cleared off the line by Aziz Behich, and Michael Thwaite was able to put the ball back into the mix.
McGarry then made amends for having earlier been beaten by Kisnorbo, the Perth midfielder hooking the ball beyond Andrew Redmayne to make it 1-1.
The away side was on level terms for less than 10 minutes before Garuccio slipped in fellow substitute Williams.
Heart's Australian marquee player prodded his first attempt straight at the on-rushing Vukovic, before leaping to nod the rebound over the stranded goalkeeper and into the back of the net.
Melbourne Heart 2 (Kisnorbo 51', Williams 82')
Perth Glory 1 (McGarry 73')
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