Fullback Awatere Kiwara crossed out wide, after second row Jerome Mamea off-loaded on the try-line, for New Zealand to lead 12-6 at half-time. Then Soosemea struck to extend the lead.
Kaufusi proved a handful for the Kiwi defence throughout the game and could not be stopped close to the line, muscling his way over for a second try.
Wallace sealed the result with a deft little grubber kick, which he regathered to score under the crossbar. The conversion - Wallace's third of the match - took the margin to double figures again enough to withstand a third NSW try this one to lock Mathew Coker.
"It was very tough," said New Zealand Secondary Schools coach Moehewa Armstrong.
"We expected New South Wales to come out with speed, but then It became a way of attrition."
"We certainly just kept coming at us and in the end, our boys really dug deep. They came in with a unity that they wanted to fight for each other right up to the last minute and that's what they did, so I'm really proud of them."
Wallace was nominated by the NSW side as the NZ player of the match, while Kaufusi was adjudged best of the guests.
The two rivals will meet again at 2.30pm Saturday on Auckland's Cornwall Park.
Last year New Zealand rallied from an 18-point half-time deficit to pip the tourists 30-22 in their one-off fixture.
NZ Secondary Schools Selection: 22 (Neal Tai, Awatere Kiwara, Lewis Soosemea & Zae Wallace tries; Wallace 3 goals) NSW Combined High Schools: 18 (Oregon Kaufusi 2 & Mathew Coker tries; Tom Steadman 3 goals)
