Oceania champions Tahiti, who had captain Nicolas Vallar sent off just before halftime, were earlier beaten 2-0 by the Solomon Islands in Honaira in the first match of the region's final round of qualifying for the 2014 finals in Brazil.
New Zealand, who qualified for the 2010 finals in South Africa, were humbled 2-0 by New Caledonia in the semi-finals of the Oceania Nations Cup in June, which cost them the opportunity of a big payday at next year's Confederations Cup in Brazil.
On Friday, first half goals from Shane Smeltz and Chris Wood settled the nerves, although the All Whites were required to do most of the defending in the second half.
"We had a lot of the first half and it probably could have been five (goals)," All Whites coach Ricki Herbert said in a telephone interview from Noumea. "But they really threw everything at us in the second half, nothing to lose I guess.
"It's always difficult to mark but those three guys at the back (Tommy Smith, Winston Reid and captain Ryan Nelsen) were really strong.
"We absorbed everything and also could have scored a couple more on the break but it was just important for us to get off to a good start. Very professional performance and pleasing (to get) three points on the board."
In Honiara, Tahiti were reduced to 10 men on the stroke of half time when Vallar was sent off for a foul on counterpart Henry Fa'arodo, who had earlier given the home side a 1-0 lead and was bearing down on goal.
Himson Teleda added the second goal after the break, to give the Bonitos an upset win in the first match of the final stage of qualifying in the Oceania region, which consists of a single pool of the four teams, all playing each other home and away.
The winner of the pool advances to face the fourth-placed team from the Central and North American confederation (CONCACAF) in a two-legged playoff for a spot in Brazil.
The second round of matches is on Sept. 11 with Tahiti hosting New Caledonia in Papeete, while New Zealand play the Solomon Islands in Auckland.