The visitors then took a surprising lead when giant midfielder Orlando Engelaar blasted home a shot from outside the box in the ninth minute.
Listed at 1.96m, Engelaar was a menace on the paddock for Melbourne and gave Wellington goalkeeper Glen Moss no chance.
Moss then gave the Heart every chance to score their second as he inexplicably left his line to try and cut off a long ball to Melbourne striker David Williams but left himself stranded as Williams lobbed it over the custodian to double their advantage.
The first spell was torrid for Wellington as they never got out of first gear in a game which featured them wearing a one-off charity strip.
Down 2-0 at the split, Phoenix coach Ernie Merrick pulled midfielder Jason Hicks and inserted teenager Matthew Ridenton to the action in a bid to shake things up.
But Ridenton was responsible for giving the ball away in the middle of the park as Williams then took the opening to score his second in the 51st minute.
The massacre didn't stop there as a Robbie Wielaert shot from distance bounced off the crossbar and in to Moss who was credited with a freakish own goal.
At 4-0 down, some of the 9726-strong crowd started to leave as they could tell it was going to be a painful final half hour.
They weren't wrong either as Williams became the first Heart player to score a hat-trick when he curled in a sensational shot in the 63rd minute.
That goal summed up Wellington's day as they hung off Williams and gave him too much time.
After Moss had pulled himself off the deck having dived in an attempt to make a save he stood with his arms out wide and questioned what the Phoenix players were doing.
There were never any decent answers supplied either as Wellington were left to contemplate their worst performance of the season.
The result leaves the Phoenix in seventh place, just outside the playoff picture.
Melbourne Heart 5 (Orlando Engelaar 9, David Williams 19, 51, 63 Glen Moss 54 og) Wellington Phoenix 0 Halftime: 2-0