The result means the Black Sticks will face Canada in a quarterfinal tomorrow.
After trailing 2-0 at the end of the first quarter, the Black Sticks rebounded well with goals to Hugo Inglis, Phil Burrows and Simon Child.
Southern striker Inglis, playing his 150th international at the age of just 24, had a big influence on the game.
''It went down to the wire. We gave them a two-goal lead and then we did enough to hold on in the end,'' Inglis (24) said.
''It was good having a win against Japan and Egypt early on and getting the six points, and it was a nice game against the Dutch, but today we were a bit up and down.
''I don't think we have reached our peak yet. It is nice to be building to our quarterfinal.''
Eighth-ranked Korea got on the front foot when Kim Seongkyu found space in the circle and scored from a reverse stick shot, giving goalkeeper Devon Manchester little chance.
The Koreans stretched their lead to 2-0 in the 12th minute when Kim Youngjin, on the angle and with immense power, struck the ball to the bottom corner of the net.
In the second quarter, New Zealand settled and started to take control of the game.
Inglis received the ball from Andy Hayward and magnificently dribbled it through a maze of Korean defenders, knocking it over the line to make it 2-1 at halftime.
The Black Sticks found the equaliser in the 34th minute when Inglis passed to veteran Phil Burrows, who hit it between the goalkeeper's legs after he was caught kneeling on the ground.
Inglis continued to have a big impact in his milestone match when a nice one-two with Simon Child ended with Child adding his name to the scoreboard in the 45th minute and giving the Black Sticks the lead.
Korea applied pressure later in the fourth quarter and the lead was snatched from the Black Sticks when Nam Hyunwoo scored from a penalty corner drag flick.
With all games in pool A now played, the Dutch finish top of the pool, followed by the Black Sticks, Korea, Japan and Egypt.
