Play had been delayed until 0300 GMT after heavy overnight rain had caused a sodden outfield.
Daren Ganga was on 31 not out and Brian Lara, who had scored just seven runs in four innings in the series, on 28 when the poor light forced the players from the field at 0510, just after they had returned from the tea break.
Play was called off for the day at about 0530.
Chris Gayle (30) was the only wicket to fall after New Zealand captain Stephen Fleming had won the toss and chosen to bowl in cool and overcast conditions.
New Zealand have wrapped up the series after a 27-run victory in the first test in Auckland and the 10-wicket win in Wellington.