The hosts led at Etihad Stadium through Archie Thompson's 19th-minute opener, before ex-Victory man Sebastian Ryall levelled with 12 minutes to go in the first half.
Extra-time looked to be a certainty after a tight second term in the elimination final before Brazilian playmaker Finkler struck in the 92nd minute to snatch a dramatic win for Kevin Muscat's men.
It could prove to be Alessandro Del Piero's last professional game, with the Sky Blues' Italian great tipped to now call time on his playing career.
Victory now face either Western Sydney Wanderers or Brisbane Roar away from home for a place in the grand final, with that fixture depending on the outcome of the second elimination final between Central Coast and Adelaide United in Gosford on Saturday.
Sydney's exit at the first hurdle of the play-offs is sure to cast more doubt on the future of coach Frank Farina, while Victory will now prepare for a tough assignment at either Suncorp Stadium against premiers Brisbane or a trip to Parramatta to take on last season's beaten grand finalists the Wanderers.
