After looking comfortable on 3-159 at tea, the Black Caps lost 7-62 in the last session before stumps after winning the toss at Queen’s Park Oval in Port of Spain, Trinidad.
Opener Tom Latham again provided the mainstay of the New Zealand innings after Hamish Rutherford, brought into the side to replace an out-of-form Peter Fulton, departed early for three, edging a drive to slip.
Left-hander Latham stroked his third half century in succession as he and Kane Williamson added 104 for the second wicket before Williamson fell on 42, hooking Shannon Gabriel to fine leg.
Latham, who scored 83 and 73 in New Zealand’s 186-run win in the first Test, departed just before tea for 82, driving Kemar Roach to gully where Sulieman Benn took the low catch.
McCullum survived just one ball after tea before he was trapped in front by Benn for four. Neesham followed seven overs later, chasing a wide ball from Jerome Taylor for Chris Gayle to take a sharp catch at first slip.
BJ Watling lasted barely two overs, edging a pitched up delivery from Taylor to wicketkeeper Denesh Ramdin, and when Sodhi was dismissed without scoring, New Zealand were floundering at 199-7.
Tim Southee (10) and Mark Craig (4) could add little to the tally, and it was left to Ross Taylor to hold the innings together.
Despite living dangerously early on, Taylor ended the day on an unbeaten 45, hitting seven fours in his 80-ball innings.
Jerome Taylor was the chief destroyer for the West Indies, finishing with figures of 4-34 off 17 overs, with useful efforts from Benn (3-73) and Gabriel (2-43).