Costa Rican duo Carlos Hernandez and Kenny Cunningham netted before half-time to set up the crucial win in front of 18,506 spectators at Eden Park.
Previously unbeaten in seven matches, a frustrated Reds outfit will return to Australia having missed the chance to move to fourth, with Awer Mabil's last-minute consolation coming too late for the tired visitors to mount a late challenge.
Busy all afternoon, Hernandez scored the first goal from a penalty and created the other in the shadow of half-time for Cunningham, who produced a slick finish.
The result boosts the Phoenix to just a point behind the Reds, who had started the round in sixth place.
Another major talking point from the match was Stein Huysegems' double blunder in front of goal just before half-time.
Within 10 seconds of madness, the Belgian striker hit the post and then the crossbar after a brilliant ball from Hernandez had completely cut United open.
Huysegems had earlier been foiled by keeper Eugene Galekovic after being put in a one-on-one situation by another great Hernandez pass.
When the ball ended up back in the penalty area, Hernandez and defender Daniel Bowles collided and referee Peter Green pointed to the spot.
Hernandez stood up, cheekily winked at Galekovic, before sending the keeper the wrong way.
At 44 minutes Hernandez again bobbed up to hurt the Reds.
In heavy traffic on halfway, he managed to get a ball to Cunningham, who sped down the touchline before cutting back to fire a shot into the corner of the net.
Although the Reds lifted briefly early in the second half, the match always belonged to Ernie Merrick's charges.
Wellington was the superior team for most of the match, and their fresh legs meant they fired six shots on target compared to Adelaide United's two.
Wellington Phoenix 2 (Hernandez 22, Cunningham 44)
Adelaide United 1 (Awer Mabil 89)
Crowd: 18,506 at Eden Park
