The home side had gained control of the match in the best-of-three-series by converting their overnight 307 for six to 441 thanks mainly to a half-century from BJ Watling.
But the tourists, who had claimed the final wicket at the end of the morning session, were unable to start their reply before tea because of persistent.
A 58-run partnership between Watling and Trent Boult for the last wicket had helped put New Zealand in charge.
Watling scored 65 and Boult was unbeaten with a rapid 38 as the home side totalled 441 in their first innings by lunch.
With the first Test in Dunedin having finished in a draw New Zealand claimed the initiative after starting the second day on 307 for six thanks mainly to a century from Ross Taylor on the opening day.
Watling, eight not out overnight, claimed a valuable half-century as New Zealand put themselves in a strong position.
Tim Southee and Ish Sodhi contributed 21 and 27 respectively before Neil Wagner fell for a duck.
But that brought Boult together with Watling and the former provided the fireworks as the latter continued to build his innings.
Watling finally fell when he was bowled by Shannon Gabriel, Tino Best claiming the wickets of Sodhi and Wagner to finish with four for 110.
Gabriel and Darren Sammy each took two wickets in the innings as the West Indies attack was made to looked ordinary by the home side's batsmen.