The European champions had numerous attempts at goal in a match marked by a myriad of missed chances before Roord headed in at the back post.
The double attacking threat of Lieke Martens and Vivianne Miedema failed to deliver despite periods of sustained pressure. New Zealand looked on course for a well-earned, but unexpected, point before conceding two minutes into stoppage time.
Dutch striker Martens had the first chance of the game, producing a good save from Kiwi goalkeeper Erin Nayler, as a pattern of missed opportunities quickly began to emerge.
New Zealand hit the crossbar in the 11th minute when a shot from Olivia Chance went over the head of Dutch goalkeeper Sari van Veenendaal, who soon after had to turn away a long range effort from Rosie White.
At the other end, Dominique Bloodworth missed a sitter from right in front of goal after a melee in the New Zealand penalty box on the stroke of halftime.
In the second half, Sarah Gregorius had a golden chance to put New Zealand ahead, but miscued her shot with only the keeper to beat. The Dutch took control for the last 15 minutes of the game, relentlessly attacking the opposing defence before finally scoring.
The Netherlands now share top place with Canada, who edged Cameroon 1-0 in Montpellier on Monday in Group E's opening game.
(Reporting by Mark Gleeson in Cape Town; Editing by Christian Radnedge)
