Victory did not have it all its own way against Rockdale City Suns before eventually finishing a 3-2 winner.
James Makarounas scored the first of his double on the stroke of half-time before Besart Berisha doubled the visitor's advantage after 50 minutes.
Marko Jesic clawed one back for the NSW Premier League side via the penalty spot just three minutes later, but Makarounas scored his second after 65 minutes to restore Victory's two-goal advantage and seemingly put the result beyond doubt.
A Leigh Broxham own goal on 86 minutes set up an intense finish, with the Suns peppering Victory's goal, but the A-League champion held on to seal a spot in the last eight of the tournament.
Western Sydney did it a little more comfortably on the Gold Coast, beating local side Palm Beach Sharks 2-0.
A goal in the first-half by Dimas Delgado and one in late the second-half from Brendan Hamill ensured the Wanderers progression in the cup competition.
Elsewhere, it was a great night for Victorian clubs with Hume City FC and Oakleigh Cannons advancing.
Hume dispatched former NSL side Sydney Olympic 3-1, with Daniel Clark, Marcus Schroen and Theo Markelis doing the damage for the home team and Dimitris Hatzimouratis scoring the solitary goal for Olympic.
Mirjan Pavlovic scored the only goal of a tight affair in Adelaide, as the Cannons pipped Metrostars FC.
FFA Cup quarter-final draw:
Melbourne Victory v Adelaide United
Perth Glory v Western Sydney Wanderers
Hume City v Oakleigh Cannons
Heidelberg United v Melbourne City
