In a match of high drama and physicality, Auckland scored after just 28 seconds, but they were reduced to nine men after Daniel Hall was given his marching orders in the 49th minute and Logan Rogerson in the 79th.
Wellington pushed hard for the equaliser and created a flurry of chances, but the visitors' defence was able to withstand every blow.
The win means Auckland are four wins from four in New Zealand derbies, and more importantly sit on top of the table with three wins and a draw to show from the first four rounds of the season.
But they will be sweating on the fitness of match day skipper Jake Brimmer, who went off in the 75th minute after appearing to dislocate his left shoulder.
Fans were barely settling into their seats when three Auckland attackers beat the hosts' defensive high line to set up Sam Cosgrove for the opening goal in the first minute.
Jesse Randall provided the assist after receiving the ball over the top, with his squared pass resulting in an easy tap-in for Cosgrove.
Wellington's reply in the ninth minute was spectacular, with Ifeanyi Eze picking off a wayward Auckland pass before unleashing a mesmerising strike from outside the box.
Randall was proving hard to stop, and he put Auckland ahead in the 34th minute when he broke the high line again before racing forward to dink the goalkeeper.
Although Cosgrove was officially awarded the goal after getting a thigh to the ball on the line while attempting to shepherd out a defender, it was Randall who rightfully received all the praise.
Hall was handed a straight red card in the 49th minute for denying an obvious goalscoring opportunity by bringing down substitute Corban Piper as he raced towards goal.
And Auckland coach Steve Corica kicked an object on the sidelines in frustration when Rogerson was sent off for a dangerous studs-up sliding tackle with 11 minutes remaining in regulation time.
It meant Auckland had to scrap for survival, and they achieved it with aplomb.
Corica believed his side were hard done by with the first red card, saying there was a Phoenix handball in the lead-up play.
"For me, we've got confirmation that the first one should have been a handball from Piper," Corica told Sky Sport.
"That means Dan Hall isn't a red card. He should still be on the pitch.Â
"By my calculation that should be our foul. I'm not sure what they looked at there but that starts everything off.
"Obviously Logan Rogerson, it looks like a red card to me. I'm OK with that one."
