The victory lifts the European champions into a tie with Canada atop Group E.
The Football Ferns, stout in defence and sharp on the counter attack, were left with nothing but disappointment.
The stars of a lively match were the two goalkeepers, Sari van Veenendaal for the Netherlands and New Zealand's Erin Nayler. Both were busy and both, at different stages, underwent on-field treatment after brave saves.
The Dutch dominated possession and goal attempts but New Zealand created three dangerous chances.
In the first half, Olivia Chance hit the bar and Rosie White drew a sprawling save from Van Veenendaal with a long-range strike.
Early in the second half Sarah Gregorius, who is of Dutch descent, shinned a volley into the ground that gave Van Veenendaal time to lunge to her right and claw the ball round the post.
At the other end, centre-backs Rebekah Stott and Abby Erceg coped well with the physical presence of Dutch forward Vivianne Miedema and the lively skills of the attackers around her.
When the Dutch did carve a clear chance, they were frustrated either by Nayler or some anxious finishing, until the final moments.
The Dutch swung one more hanging cross to the far post where Lineth Beerensteyn bulleyed Ali Riley into a tame header back across the goal and Arsenal's Roord guided the ball past the advancing Nayler.
Later in the day Group F kicks off with Chile facing Sweden in Rennes and the USA and Thailand end the first set of games in Reims.