The New Zealand cricketers have managed to extend the second Test into the final day in Port of Spain, but the West Indies remain in the driving seat.
The Blacks Caps are 257 for eight at stumps, a lead of 18 runs, with BJ Watling on 38 and Mark Craig 26.
The pair have so far batted 28 overs for a ninth-wicket partnership of 45 runs.
Earlier Tom Latham made 36, Kane Williamson 52 and Ross Taylor 36.
Pace bowler Kemar Roach has three wickets and Jerome Taylor and Sulieman Benn two each.
New Zealand won the first match in the three-Test series.