The result moves Adelaide level with the Phoenix in fourth place, with three regular season matches remaining.
The home side enjoyed an explosive first half, racing to a 3-0 lead before going down to 10-men.
Mark Rudan's Phoenix side were in fine form heading into the fixture, having scored 15 goals in three games which was a record for the competition.
Despite the confidence, Adelaide were the team that started off with the impetus to get the first goal and it wasn't long until they achieved it.
10 minutes in and Michael Marrone headed in to give his side the lead after a Craig Goodwin cross.
Wellington Phoenix attacker, David Williams, looked to attack the backline of Adelaide and very nearly dispossessed Paul Izzo, only for the goalkeeper to clear it out for a throw-in.
The home side struck again to double the lead shortly after, as Apostolos Stamatelopoulos arrived first to a deadly cross from former Wellington Phoenix player, Scott Galloway.
Roy Krishna provided hope in the attacking third as he attempted to penetrate the Adelaide defence, but Isaias was quick to return to his defensive duties and clear the danger.
As the half time whistle grew nearer, Wellington Phoenix found themselves growing further into the game. Sarpreet Singh provided a glimmer of hope after he received the ball in space and drove toward the Adelaide goal, only for his effort to go over the bar.
The second half began and the Phoenix were a different beast and the intentions were clear to see, scoring a goal to cut the hosts lead.
Despite last-minute half chances for Wellington Phoenix, Adelaide held on to keep all three points as the game ended 3-1 to Marco Kurz's side.