Their passing lacked cohesion, possession was regularly and cheaply given away and there was nothing to enthuse about in the attacking third.
Given the performances of the last three weeks during which the Phoenix had scored an A-League record 15 goals, it was a curiously flat display.
In the ten minutes before the break though, Wellington finally got going with Liberato Cacace testing goalkeeper Paul Izzo with a low drive before Antony Golec had a header cleared off the line.
Just as the visitors seemed to have gained some traction, Stamatelopoulos made it 3-0, his powerful header squirming under the outstretched body of Phoenix goalkeeper Filip Kurto and just crossing the line.
But Stamatelopoulos immediately went from hero to villain with a studs-up challenge on Mandi earning him a straight red card in the shadows of halftime, leaving his side to negotiate the second half with just ten men.
Phoenix coach Mark Rudan rolled the dice early in the second spell, introducing attackers Cillian Sheridan and Max Burgess.
With a numerical advantage and Burgess in particular adding significant creativity and spark, the Phoenix laid siege to a packed Adelaide defence in an attempt to reduce the deficit.
A delightful pass from Burgess put Sheridan through one-on-one but after the Irishman rounded Izzo he declined to shoot from a narrow angle, instead laying the ball into the path of David Williams who blazed over from a handy position.
Wellington's first goal finally arrived after 73 minutes when Mandi's low drive through a crowded penalty area hit the post and rebounded into the path of Sheridan who tapped in his maiden Phoenix goal from close range.
The chances continued to come for Wellington with Burgess at the heart of their best attacking moments.
With five minutes left, Kopczynski had the ball in the net after a goalmouth scramble, but the goal was chalked off for offside.
Despite their dominance, time ran out for the Phoenix who were left to rue their poor first half and contemplate an 11th straight winless outing against Adelaide.
The Phoenix will remain in Australia ahead of Friday's clash with Brisbane Roar before returning home for what is shaping as a pivotal meeting with Melbourne City on Easter Sunday.
Adelaide United 3 (Stamatelopoulos 2, Marrone)
Wellington Phoenix 1 (Sheridan)
