Kane Williamson's career-best 161 not out guided New Zealand into a 307-run lead going into the fifth day of the series decider against West Indies in Barbados.
No 3 Williamson, on 58 overnight, batted throughout a rain-shortened day four of the third Test as New Zealand closed on 331-7 in their second innings.
The tourists lost skipper Brendon McCullum in the fourth over of the day, lbw to Kemar Roach for 25 to end a fourth-wicket stand of 67.
New Zealand's lead was only 111 at that point but Jimmy Neesham joined Williamson in a 91-run partnership for the fifth wicket.
Neesham's 51 included four sixes and ended with a catch to short cover off the bowling of seamer Jason Holder (2-26).
Williamson completed his seventh Test hundred before lunch and, after Neesham's exit, he pressed on in the company of BJ Watling (29) during the afternoon session.
Fast bowler Roach (4-55), playing on his home patch, made Watling his 100th Test wicket - the 19th West Indian to reach that milestone - before heavy rain arrived at the Kensington Oval to prompt an early tea with New Zealand on 314-6.
The weather cleared sufficiently to get a few more overs in late in the day, West Indies adding the wicket of Tim Southee (7), Jerome Taylor's first of the match.
But the rain soon returned to end proceedings for the day and leave match - and series - finely poised.
The three-match series is level at 1-1 after New Zealand won the first Test by 186 runs in Jamaica and West Indies responded with a 10-wicket success in Trinidad.