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The resounding win moves Victory up to second in the A-League table, although they could end up as low as fourth if Western Sydney Wanderers and Central Coast Mariners both pick up three points later today.
Melbourne dominated proceedings from start to finish in New Zealand, taking the lead after just 48 seconds thanks to Archie Thompson's eighth goal of the campaign.
Thompson completed a one-touch move by thumping James Troisi's low first-time cross into the roof of the net from close range.
Troisi doubled Melbourne's lead on 29 minutes, firing a left-footed shot into the top corner of Jacob Spoonley's goal from an acute angle.
It was 3-0 on the stroke of half time following another intricate passing move, which ended with Finkler Guilherme beating Spoonley with a dinked finish.
Wellington were booed off at the interval, but that failed to shame the hosts into improving significantly in the second period.
Mark Milligan sent Spoonley the wrong way and emphatically converted the resultant spot kick into the top corner.
Victory's fourth meant that there was no way back for Wellington and the home fans therefore decided to embrace their side's mediocrity, singing 'Always Look on the Bright Side of Life', as well as performing a conga.
Wellington did manage to muster a consolation goal in the final minute of stoppage time. Jeremy Brockie connected with a deep corner kick to send a left-footed volley back across goal into the far top corner.