Netherlands opened the scoring early in the first quarter when Caia van Maasakker's hard penalty corner flick picked up a slight deflection and soared into the top left corner.
The Black Sticks defended hard throughout the quarter and then managed to turn the pressure into some impressive attacking moves.
Webster drew the score level in the 16th minute when she pounced on her own deflected shot and hammered home on the reverse stick.
The Dutch pulled ahead once more just two minutes out from halftime after Kelly Jonker slipped a shot past Sally Rutherford in goal from a hard crash ball into the circle.
The second half belonged to the world's top side, with further goals coming from Ellen Hoog and a second for Jonker.
New Zealand put together some impressive phases of play and had several clear shots at goal but couldn't break the Dutch defence.
The Black Sticks have a rest day tomorrow before their final pool game against Germany at 10:45am on Wednesday (NZ time).
BLACK STICKS 1: (Petrea Webster)
NETHERLANDS 4: (Kelly Jonker 2, Caia van Maasakker, Ellen Hoog)
Halftime: Netherlands 2-1