Neesham’s knock came at just the right time as the Kiwis recovered from losing some early wickets to post an imposing total.
The morning session began poorly for the visitors, as Kane Williamson was removed having added just eight runs to his overnight total to be dismissed for 113.
Sulieman Benn fooled the right-hander with a slider, which Williamson left alone as it cannoned into his off stump to leave New Zealand 259-3.
That brought Brendon McCullum to the crease, but another wicket would fall soon after as Ross Taylor chipped an easy catch to Kirk Edwards at mid-wicket off the bowling of Shane Shillingford to depart for 55.
West Indian hearts were in their mouths as the ball rebounded offRamdin’s chest, but the ball looped upward and was held easily by Chris Gayle at slip.
New Zealand’s overnight total of 252-2 had become 279-5 in almost no time as their batting collapsed.
From there, it was left to BJ Watling and Neesham to battle through to lunch, which they did to finish on 299-5 in a session that belonged to the hosts.
After the break, things got much better for the visitors as Watling andNeesham piled on the runs.
The pair put on 129 runs in just 35 overs and passed their fifties with ease, with Neesham looking impressive as he maintained a strike rate of well over 50.00.
He finished the afternoon unbeaten on 85, while at the other endWatling produced another effective innings to finish on 56 not out.
The West Indians ended the session looking demoralised and keen to collect their thoughts in time for the evening period of play.