The New Zealand cricketers will start the final day of the opening test in Dunedin on 44 for 2, a lead of 69 over the West Indies.
Jerome Taylor scored a his maiden test century for the tourists, coming to the wicket at 173 for 6, still 189 runs behind the New Zealand first innings total of 365, Taylor bludgeoned 17 fours and three sixes on his way to 106.
His partnership with veteran Shivnarine Chanderpaul, who was last man out for 76, took the West Indies to a first innings total of 340.
At the wicket Tim McIntosh is on 28 and Daniel Flynn not out four.
The Black Caps lost opener Jamie How bowled by Daren Powell for 10 and night watchman Kyle Mills the very next ball, also bowled by Powell.
In the Windies innings Dan Vettori finished with 6 wickets for 56.