Victory started the game on the front foot with Fahid Ben Khalfallah having two long-range strikes on goal, the first of which curled marginally over the crossbar.
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Brisbane improved though, and shortly after the quarter-hour mark, Steven Lustica came agonisingly close to giving his side the lead with a free kick that struck the woodwork.
Back came Melbourne with Ben Khalfallah forcing a solid save out of Ben Young, before Roar midfielder Dimitri Petratos sent a shot just off target.
However, in first-half injury time, Melbourne went ahead thanks to a penalty from Milligan, who stepped up to take the kick after Carl Valeri was adjudged to have been fouled inside the area.
Jerome Polenz came off the bench early in the second half for the hosts, and he tried his luck with a long-range drive, which curled just wide of the post.
Victory tried to extend their lead inside the final 15 minutes as Guilherme Finkler came on to add some more pace going forward, resulting in him setting up Ben Khalfallah for a header, but his finish went high of the crossbar.
Besart Berisha had the ball in the back of the net late on, thinking that he had doubled the visitors' advantage, but he was offside as Finkler picked him out with a through-ball, ruling out his chip past the keeper.
With just one round of fixtures remaining, the win all but guarantees that Victory will finish top of the table, leaving them three points clear of Sydney but with a better goal difference.