Neesham's innings of 107 and a 201-run sixth-wicket partnership with B.J. Watling (89) lifted the Black Caps to a total of 508 for seven declared.
Left to negotiate a tricky nine overs before the close of play, West Indies reached 19 without loss with Chris Gayle, in his 100th Test match on his home ground, to resume on the third morning with Kieran Powell.
Despite an encouraging effort in the morning session when three wickets fell for 20 runs to have New Zealand at 279 for five from their overnight position of 240 for two, the West Indies bowlers again laboured on a benign pitch throughout the afternoon.
Neesham, the 23-year-old left-hander from Auckland who launched his Test career with a century in a drawn match against India in Wellington last February, mixed watchful defiance with periods of bold aggression.
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