The Victory were handed the opportunity to take the lead when Jason Geria was brought down in the box and a penalty was awarded. Besart Berisha took the spot kick and sent Eugene Gakekovic the wrong way to put his side ahead.
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The home team doubled their advantage through Oliver Bozanic as he managed to catch out Gakekovic at his near post to beat the keeper with a quickly taken free kick.
In the second half, Guilherme Finkler set up Fahid Ben Khalfallah who forced a save out of Gakekovic as Victory pushed for a third, but during the closing stages, Adelaide began to threaten, with Craig Goodwin and Isaias both going close.
With three minutes remaining, they halved the deficit when Marcelo Carrusca netted from the spot to set up a tense finish, but Melbourne held on to leave Adelaide at the foot of the standings.