Roach claimed four wickets, while Best and Narsingh Deonarine chipped in with two scalps each. For the visitors Martin Guptill was the top scorer with 71.
Earlier, Guptill and Ross Taylor both hit half centuries as New Zealand recovered from a shaky start to reach 152 for 3 at tea. Opener Guptill struck an unbeaten 62, his third straight fifty, while Taylor contributed an enterprising 60.
The pair shared a third wicket stand of 103 that rescued the Kiwis after they slipped to 11 for 2 inside the first half hour, losing Brendon McCullum and BJ Watling.
Best, who along with Roach set the innings back after the hosts won the toss, broke the blossoming stand midway through the second session.
Taylor tried to cut one that angled into him, cramping him for room, and edged through to wicketkeeper Denesh Ramdin.
But Guptill found another solid ally in Kane Williamson, who went to the break undefeated on 17.The West Indies should have had further success five minutes before tea but Narsingh Deonarine put down a sharp, head-high return catch off Williamson.