Just seven overs were bowled after tea, leaving the tourists 331-7 with a lead of 307 at the close of play on the penultimate day in Barbados.
The day started well for New Zealand as Kane Williamson helped them pile on the runs in the morning session, completing his seventh century for the team in the process.
Williamson was ever-present at the crease throughout the day, finishing on 161 not out, while Jimmy Neesham notched up a half-century.
BJ Watling provided a brief partnership in the afternoon session before being dismissed by Kemar Roach for 29, while Tim Southee was the only wicket to fall after tea having been caught and bowled by Jerome Taylor.
Roach has been the pick of the bowlers in the second innings so far for the hosts, claiming four wickets for 55 runs.
The match is due to reach its conclusion tomorrow.