Instead, it was the home team's debutants, Belgian Stein Huysegems and Wellington teenager Louis Fenton, who found themselves on the scoresheet as the Phoenix dominated at Westpac Stadium.
All the talk in Australia has centred on the arrival of Del Piero, Emile Heskey and Shinji Ono, allowing Huysegems, rising star Fenton and the Phoenix to fly under the radar.
Wellington dominated from the start and created a plethora of chances, particularly in the first half when they hit the woodwork twice and had a goal disallowed before Huysegems opened the scoring two minutes before the break.
He had already headed one wide and hit the woodwork by the time he gathered Manny Muscat's ball over the top and calmly finished past Ivan Necevski.
The Phoenix made the game safe in the 75th minute when Muscat dispossessed Del Piero and fired a pinpoint ball into the box which a diving Fenton headed home before running to celebrate with the crowd.
In Saturday's other game Western Sydney Wanderers began life in the A-League with a goalless draw with Central Coast at Parramatta Stadium.
There were few chances for either side, although Mariners goalkeeper Mathew Ryan was the busier of the two goalkeepers denying Mark Bridge and Aaron Mooy in the first half.
Michael McGlinchey did go close for the Wanderers in the second half when he found some space to shoot from a narrow angle and forced a save from Ante Covic, but neither side could complain with the result.