Adelaide started strongly and took the lead after just seven minutes when Craig Goodwin, given too much space 10m out, volleyed a cross which diverted in off teammate George Blackwood.
The home team's dominance continued throughout the first half, with the shot count 16-4 at the break (7-1 on target).
While the Phoenix failed to fashion a single decent scoring opportunity in the first half, there were two glimmers of hope for the visitors.
The first was that Adelaide had failed to convert their wealth of chances into a more commanding lead they probably deserved.
The second was that Adelaide keeper James Delianov was forced off after dislocating his left shoulder in a challenge with Ben Waine. On came Steven Hall, the youngest keeper in A-League history, aged 16 years 350 days.
But Wellington were unable to capitalise on either count.
Phoenix coach Ufuk Talay — frustration personified on the sideline — made three changes at halftime, further building on the youthful theme: on came Finn Surman (18), Oskar Van Hattum (19) and Nicholas Pennington for skipper Alex Rufer, Jaushua Sotirio and Callan Elliot.
Hopes of getting back into the match evaporated when referee Daniel Elder awarded a debatable 54th-minute penalty for an alleged Tim Payne foul on Blackwood.
Fifteen minutes later, Adelaide had a second penalty, this one for an obvious James McGarry foul on Bernardo Oliveira. More frustration — McGarry was dragged immediately and Goodwin again scored from the spot, this time rolling the ball into the other corner.
The rout was complete with a fourth in the 80th minute, Javi Lopez scoring his first goal in eight years when he ghosted through a static Phoenix defence to volley home.
Adelaide United 4 (George Blackwood 7, Craig Goodwin 54 pen, 69 pen, Javi Lopez 80)
Wellington Phoenix 0