Since 2010, it is a first appearance for New Zealand which made it three wins out of three in Oceania qualifying group stage, Reuters reported.
The All Whites now move on to next year’s four-team final stage of qualifying along with New Caledonia, Fiji and Tahiti, who earlier beat Vanuatu 2-0 at the same Auckland stadium to secure their passage.
New Zealand will play Fiji and New Caledonia will take on Tahiti in the semi-finals in Wellington on March 21 with the final taking place at Auckland’s Eden Park three days later.
The winner of the final qualifies directly for the 2026 World Cup finals with the losers going into an intercontinental playoff tournament featuring six teams from around the world.
After beating Tahiti 3-0 and Vanuatu 8-1 in their previous Group B games, New Zealand were already assured of a spot in the final stage before they kicked off against winless Samoa at Mount Smart Stadium.
The heroics of Samoa goalkeeper Pele Eti Fatu kept them at bay until the 24th minute when midfielder Callum McCowatt finally slid the ball past him.
Wood, who has been in rare goalscoring form for his English club Nottingham Forest, clipped a McCowatt pass into the net four minutes later and added his second in the 34th minute after being found free in front of goal by Matthew Garbett.
The 32-year-old, who played as a teenager in New Zealand’s 2010 World Cup campaign in South Africa, scored his third with a volley in the 61st minute with Marko Stamenic adding a fifth a minute later.
Wood was substituted in the 64th minute, having contributed six goals over the three group matches to take his career tally to 41 in 80 internationals.
Francis de Vries, Eli Just and Ben Waine from the penalty spot rounded out the scoring as the mostly amateur Samoans tired in the latter stages of the contest.
"It doesn’t matter how they come or in what fashion, we just need to tick off wins," said Wood.
"That’s the results business that we re in at the moment to get to the World Cup. We’ve got a semi-final to go and we need to win that to go through the final. And then win that to go through to the World Cup.
"So we’re looking forward to the challenge ahead."
New Zealand have been the dominant force in Oceania football since Australia left for Asia in 2006 but have lost out in intercontinental playoffs in their last three attempts to qualify for the World Cup.
The expanded 2026 tournament means direct passage for the best team from Oceania and the New Zealanders will be strong favourites to book a third trip to the finals.
Tahiti earlier kept alive their dreams of a first trip to the finals in a winner-takes-all clash against Vanuatu courtesy of an early Johnathan Spokeyjack own goal and a second-half penalty from striker Benoit Mathon.
Fiji and New Caledonia played out a 1-1 draw in Port Moresby on Sunday which assured their progress from Group A and ended the hopes of Solomon Islands and hosts Papua New Guinea.
