The Black Sticks, ranked three places below their opponents at eighth, scored through Andrew Hayward (fourth minute) and Dean Couzins (22nd) in their third Pool A match.
Korea pulled one back, Lee Nam Yong scoring from a penalty stroke in the last minute.
The Kiwis defended their citadel admirably well against the Koreans, who did most of the attacking in front of a handful of spectators at the Major Dhyan Chand stadium.
The victory kept New Zealand in contention for a semi-final berth. They have two wins and a loss from three matches, and two more matches to play -- against Argentina and Germany [ Images ].
With a draw and a win from three matches, Korea are not out of contention but they will find it difficult to make it to the semi-finals as they play Canada [ Images ] and the Netherlands in their remaining matches.
Korea have themselves to blame, as they did most of the attacking throughout the match and failed to score from seven penalty-corners they got, six in the second half.
New Zealand, who had made it to the World Cup through a qualifier, took the early lead when Andrew Hayward scored from a penalty-corner in the fourth minute.
Korea pressed hard for an equaliser but their forwards failed to give the finishing touches and the Kiwi defenders maintained tight man-marking, denying their opponents space and penalty-corners they were looking for.
Korea could not convert their only penalty-corner of the first half, in the ninth minute, and in the 11th minute a nice reverse stick shot from their hard-working captain Jong Ho Seo was too high to create any problem for Black Stuis goalkeeper Kyle Pontifex.
Against the run of play, New Zealand got a penalty stroke in the 22nd minute and captain Dean Couzins did not make any mistake to take his side to 2-0 at the breather.
The Koreans regrouped themselves in the second session and New Zealand had mostly to defend inside their own 25 yards.
Shin Seok Kyo's side wasted seven penalty-corners in the second session, either finding a defender or the goalkeeper or failing to stop the ball to take the penalty-corner hit.
At the fag end of the match Korea were awarded a penalty-stroke by Indian referee Satinder Kumar, which Lee Nam Yong converted. But that was too late in the day.