Winger Fabio Ferreira was the last-gasp hero for the home side, scoring in the dying moments to help United climb into third position.
Marcelo Carrusca had earlier broken the deadlock with the fifth-fastest goal in A-League history - just 26 seconds into the contest.
But things progressively got worse for United, 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 taken to hospital, before 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. Ferreira then earned a point late on.
