The Kiwis chased down the target of 152 with one over to spare with Brendon McCullum anchoring the innings with a 45-ball knock that he made with the help of four boundaries and three sixes at the Zahur Ahmed Chowdhury Stadium.
New Zealand lost their opener Martin Guptill (9) cheaply in the fourth over but they were never in trouble as the inexperienced Dutch bowlers came up short.
When he was out in the 17th over, after sharing a 46-run stand with Corey Anderson (20 not out) for the unbroken fifth wicket, New Zealand were just 18 runs away from victory from 19 balls with six wickets in hand. Anderson took New Zealand score past the target by reaching 152 for four in 19 overs.
For the Netherlands, Timm van der Gugten grabbed three wickets for 30 runs, while Logan van Beek got one.
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Earlier, Tom Cooper's unbeaten 40 off 23 balls lifted the Netherlands to 151 for four in their allotted 20 overs.
Copper, who hit four boundaries and two sixes in his unbeaten knock, shared 60 runs for the fourth wicket with captain Peter Borren (49) after the Netherlands were put into bat.
The Netherlands were slow in their first 10 overs, scoring just 62 for two wickets, but accelerated in the second half of their innings. Openers Stephan Myburgh and Michael Swart contributed 16 and 26 respectively.