The Black Sticks scored their third seven minutes into the second half when Andy Hayward converted a penalty corner with a powerful drag flick.
Although Korea forced two penalty corners late in the match, New Zealand were convincing and the final result was never in doubt.
"At times we were a little bit sloppy late in the game, so we will look at that,'' Batch said. "We are always looking for improvements but, overall, it is a huge morale booster to beat a quality opposition like Korea.''
The Black Sticks play tomorrow night (11pm) against India who, like New Zealand, have one win and two defeats.
Australia top the table followed by Malaysia on seven points, with New Zealand, India, Pakistan and Korea all with one win and three points.
New Zealand 3 (Hugo Inglis, Cory Bennett, Andy Hayward) Korea 0. HT: 2-0.