The Newcastle United striker nodded in a header on the cusp of halftime to draw level with Vaughan Coveny on 29 goals, then curled in a shot in the 73rd minute to claim the record outright.
"It means a lot. It's been sought after for a very long time," said 30-year-old Wood.
"I dreamed as a kid trying to get to it, so to break it is fantastic and hopefully I can add a few more goals across the course of my career."
Wood may not have too long before boosting his tally, with New Zealand to play world No.153 New Caledonia in their third and final Group B game on Thursday.
Wood scored his first international goal as an 18-year-old in a 1-1 draw with Honduras in 2010, heading in a Jeremy Brockie cross and celebrating by dropping his shorts to reveal white and red underwear emblazoned with 'Woodzee'.
His celebrations on Monday were more subdued.
"I'm glad I'm a bit more mature now," said the tall forward.
"It's all about the team and winning at this point in time, especially in a tournament like this.
"With semi-finals and a final it means so much more to get to the next round on the World Cup qualifying stage, it's not about the goals."
New Zealand, easily the strongest soccer nation in the Oceania region, beat Papua New Guinea 1-0 in their opener on Friday.
The top two teams of the tournament's two groups advance to semi-finals on Sunday before the March 30 final.
The winner advances to an intercontinental playoff against the fourth-placed side from the CONCACAF region, which features nations from North and Central America, and the Caribbean.
New Zealand were the last Oceania team to qualify for the World Cup when they made the 2010 finals in South Africa.
