A 20th-minute red card for Heart defender Patrick Kisnorbo changed the game before Mitch Nichols netted a brace and James Troisi also scored, while Nick Kalmar claimed a consolation goal late on for John Aloisi's men.
The loss is sure to increase the pressure on Heart coach Aloisi despite the circumstances, with his team yet to win in 11 games this season and sitting last.
They are without a triumph in their past 16 matches, while the Victory jump to third in he table.
Despite the hosts' promising start, the game turned in favour of the away side when Kisnorbo was dismissed for a studs-up challenge on Connor Pain.
An error from Andrew Redmayne led to the opener as his dreadful low clearance fell for Mark Milligan, whose first-time pass found Nichols - kept onside by Patrick Gerhardt - to place past the goalkeeper.
Harry Kewell went close to an equaliser early in the second half as his strike from inside the area whistled past Nathan Coe's left post.
Troisi struck his seventh goal of the campaign to go top of the A-League scoring charts just before the hour mark, and Nichols complete his brace just four minutes later.
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