Del Piero finally found form after an injury-plagued season to score in the 20th, 23rd, 39th and 70th minutes, giving Sydney an emphatic win which thrust it away from the foot of the A-League table.
Sydney is paying Del Piero a reported $4 million on a two-year contract to be its marquee player in the 10-team Australian league. The investment seemed unwise as Sydney slumped to the bottom of the league and as Del Piero battled hamstring and other injuries.
But his form on Saturday echoed his glory days at Juventus, for whom he scored a record 513 goals in 208 premier matches.
"I felt free in my mind today for sure," said Del Piero who lifted his tally of goals for the season to nine. "It's a day from the heavens because when you score four, for sure it's a great day."
The win was Sydney's largest ever in the A-League and, in part, counter-balanced its 7-2 loss to league-leading Central Coast in round five.
Del Piero's performance in front of 12,691 fans was described as one of the best individual efforts ever seen in the A-League.
The 38-year-old striker led a much-improved team performance, providing the finishing touches in a win that lifted Sydney as high as sixth place, pending the outcome of other matches in the 17th round.
For Wellington, the loss ensured it equaled its worst-ever losing streak of four matches and left it resolutely anchored at the bottom of the table.
Sydney overwhelmed Wellington, racing to 5-0 after only 39 minutes. Joel Griffiths, playing his first A-League match in four years after joining Sydney from China, seemed to provide the spark that ignited his team.
He opened the scoring in the 11th, with a goal that came from slick combination with Del Piero. The Italy star delivered a superb, lofted through-ball from halfway and Griffith delivered the final touch.
Del Piero was then the star attraction, providing the flood of goals on which Sydney's win was based.
Ben Sigmund pegged one goal back for Wellington late in the match, before former Panama international Yairo Yao added to Sydney's tally.
Wellington's loss increases pressure on coach Ricki Herbert - who is also the New Zealand coach - and on the club's new owners who have insisted on a policy of total football. The playing style, implemented from the boardroom, has not sat well with the Wellington players.
Herbert said he was determined to lead Wellington out of its slump.
"That's the most disappointing performance from a team that I've had at the football club," he said. "It was totally unacceptable at both ends of the pitch."
On Friday, the Melbourne Heart upset second-placed Adelaide 2-0 to ensure Central Coast stayed atop the table for another week.
Melbourne's win, which was its best result in an inconsistent season, was accompanied by bad news as its Brazilian captain, Fred, was sidelined for a month by a quadriceps injury.
Central Coast drew 0-0 with Newcastle to hold onto first place. The draw and Adelaide's loss left Central Coast three points clear at the top.
The Melbourne Victory remained in third place, two points behind Adelaide, after a 1-0 win at Perth. The only goal of the match came in the 24th minute when defender Scott Jamieson deflected a cross from Marco Rojas into his own net.
Western Sydney Wanderers came from behind to beat Brisbane 2-1 on Sunday to stay in fourth place, with goals from Mark Bridge and Youssouf Hersi cancelling out Mitch Nichols' early goal for the hosts.
The Wanderers are now eight points clear of the fifth-placed Melbourne Heart and Newcastle, which filled out the top six.