Winger Fabio Ferreira was the last-ditch hero for the 10-man Reds, scoring in the dying moments to help United climb their way out of a 2-1 hole and into third position on the ladder.
Ferreira produced the miracle but it was Marcelo Carrusca who struck the initial blow, with the the fifth-fastest goal in A-League history - just 26 seconds into the contest - to send the home fans into delirium.
But things progressively disintegrated for the Reds, whose top-two prospects looked gone before Ferreira's stunning equaliser.
Michael Marrone sustained a suspected fractured leg in the fourth minute, the accomplished right back stretchered off the field and taken to hospital, but the near-fatal implosion came in the 35th minute when Tarek Elrich was given his marching orders after conceding successive penalties, the second one for a nasty headbutt on Aziz Behich.
David Williams slotted the first penalty before being denied with his second, but Mate Dugandzic's 42nd-minute strike gave Melbourne the lead at half-time.
The Heart moniker was apt considering the way they fought back from a nightmare start in which Carrusca, evoking memories of former Red Louis Brain's 11-second goal almost a decade ago, finished with a neat left-footer after a fine cross from Elrich, the visitors yet to touch the pill.
Played through by Nigel Boogaard in the 21st minute, Carrusca had a crack at a brace but scooped his shot high.
Jeronimo Neumann, substituted on for Marrone, came agonisingly close to making it 2-0 when he mopped up following Melbourne's defensive mix-up and cracked a volley into the right upright.
Meanwhile, the Heart maintained their focus and were playing some reasonable football with big man Orlando Engelaar looking dangerous in attack.
The match took a violent turn in the 33rd minute when Elrich conceded a penalty after a reckless challenge on Stefan Mauk with Williams coolly slotting it past Adelaide custodian Eugene Galekovic.
Moments later, Elrich's night was over, the defender handed his second yellow in as many minutes for making head contact on Melbourne left back Aziz Behich.
Williams stepped up for another penalty but this time Galekovic was up to the task, conjuring a magnificent right-handed save.
Galekovic and Michael Zullo were both booked for voicing their dissent, United racking up four yellow cards in the space of five crazy minutes.
A series of scuffles ensued before referee Ben Williams summoned rival captains Galekovic and Robbie Wielaert in an attempt to restore order.
Adelaide were frazzled and out of control and the Heart took advantage, stealing the lead in the 42nd minute when the dangerous Dugandzic volleyed home following a goalmouth scrimmage.
Galekovic pulled off another fine stop to deny a Mauk-Behich one-two in the 56th, before Melbourne goalkeeper Tando Velaphi showed similarly great athleticism and anticipation in denying Jeronimo's swerving attempt two minutes later.
Adelaide had clearly regrouped and displayed cooler heads for the majority of the second half.
They very nearly tied proceedings in the 76th minute when Jordan Elsey's flying nod crashed into the crossbar, Awer Mabil's follow-up reflex collected by Velaphi before Jeronimo's angled shot in the 86th missed by a coat of varnish.
The home side was attacking in droves but it looked in vain until Mabil, on the angle, squared one to Ferreira who instinctively pulled the trigger and sparked wild sideline celebrations from Adelaide coach Josep Gombau and his relieved team.
Adelaide United 2 (Carrusca 1, Ferreira 90+2)
Melbourne Heart 2 (Williams 33pen, Dudzantic 42)
