Del Piero scored Sydney's first two goals, his second coming courtesy of a sublime free-kick, and set up the hosts' third for Sebastian Ryall in wet conditions at Allianz Stadium on Sunday.
Ali Abbas was also on target for Sydney, who now sit three points clear of seventh-placed Newcastle Jets with one game of the regular season remaining, while Carlos Hernandez's penalty represented little consolation for a Wellington side that can no longer make the top six.
Persistent afternoon rain ensured a pitch inspection was required before the game could be given the go-ahead.
Del Piero opened the scoring from the penalty spot 12 minutes prior to the interval after going down under a challenge from Jeremy Brockie.
The Italian then found the net again on the stroke of half-time with a glorious curling free-kick from 20 yards that left Phoenix goalkeeper Glen Moss with no chance.
Wellington looked to have given themselves a lifeline when Brockie was fouled by Nikola Petkovic and Carlos Hernandez fired home the game's second penalty.
Yet Sydney made it 3-1 almost immediately as a flowing move ended with Ryall converting a delightful first-time pass from Del Piero.
A fourth home goal arrived on the hour mark when Abbas unleashed a stunning strike into the top-right corner from the edge of the penalty area.
Sydney host Perth Glory in their final match of the regular season on Sunday and will already be assured of a top-six place by then should the Jets fail to beat Adelaide United on Friday.
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