The Victory scored twice in the final 15 minutes to share the spoils before a record A-League crowd in Adelaide of 16,504 spectators at Coopers Stadium.
The Reds, with Sergio Cirio scoring from a questionable penalty and Jeronimo Neumann tapping-in from close range, appeared set to bank consecutive home wins to open their campaign.
But Melbourne substitute Guilherme Finkler netted in the 79th minute and James Troisi equalised three minutes before fulltime of a pulsating fixture.
Melbourne and their coach Ange Postecoglou, in possibly his last match in charge of the Victory as he eyes the Socceroos' coaching job, could have won if not for rotten first-half luck.
The visitors were unlucky to concede the penalty and also had a clear-cut Mitch Nichols goal disallowed by a referee's error.
Argentine striker Jeronimo featured in the two opening goals, creating the first when awarded a dubious penalty.
Jeronimo and Victory goalkeeper Nathan Coe steamed at each other, with the ball between them, in the 20th minute and the Reds' frontman milked slight contact, diving forward, and referee Alan Milliner awarded a penalty.
Adelaide recruit Sergio Cirio scored twice from the spot: his initial conversion was disallowed, then he fooled Coe with a shrewd second attempt, aimed in a different direction than the first.
Two minutes later, Jeronimo goaled after Adelaide's lively substitute Awer Mabil launched a speculative shot from just inside the box.
The ball deflected from Melbourne defender Adrian Leijer, struck the near post and, by chance, fell to Jeronimo who tapped-in.
Melbourne should have reduced the deficit in the 35th minute when Archie Thomson, after a piercing run, had Reds' goalkeeper Eugene Galekovic beat but elected to feed Nichols instead.
Nichols scored from five metres, only to be incorrectly ruled offside.
Melbourne turned the tide in the second half but a series of shots - from Leijer, Troisi and Kosta Barbarouses - all narrowly missed.
But substitute Finkler's 79th minute score, from a classy low blast on the turn, gave the visitors hope.
And three minutes into injury time, a Troisi scorcher hit the cross-bar and barely bounced over the line for the equaliser.