The Scots were 12 for four after new ballpair Trent Boult and Tim Southee took two wickets apiece early.
The saving grace for Scotland was a 97-run stand for the fifth wicket between Matt Machan and Richie Berrington, who both completed impressive half centuries.
New Zealand next face England in Wellington on Friday while Scotland have a few days off before also playing England in Christchurch on Monday.
Image 1 of 13: Trent Boult of New Zealand successfully appeals for the wicket of Hamish Gardiner of Scotland during the ICC Cricket World Cup match. Photo / Getty Images