Sydney's Mickael Tavares had the first opportunity of the match but he was denied after connecting with a set piece, but after clear-cut chances proved hard to come by, Sydney were reduced to 10 men as Alex Gersbach was sent off for a high challenge on James Jeggo.
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Ten minutes into the second half, Vedran Janjetovic made a save from Sanchez, who must have thought he would score from point-blank range, but shortly after the hour mark, Adelaide finally took the lead through Jeggo, who converted the rebound after he had seen his half-volley hit the woodwork.
However, despite their numerical disadvantage, Sydney required just eight minutes to equalise thanks to Filip Holosko, who chested the ball down before hitting it into the far corner.
It appeared as though the game would end in a draw, but deep into added-on time, Adelaide were awarded a penalty, which was duly dispatched by Carrusca to give the home side a dramatic victory.