The collapse mirrored that of the second match in which the West Indies fell from 0-63 to 138 all out as New Zealand won by five wickets, levelling the series after losing the first match by seven wickets.
New Zealand's run chase was cautiously paced at 3.5 runs per over and ended in the 40th over at 4-141, with 63 balls remaining.
Henry Nicholls made 24 and Will Young 23 in a solid partnership for the first wicket, Daryl Mitchell made 28 in the middle of the innings and Tom Latham and Dean Foxcroft saw New Zealand home in an unbroken partnership of 52 for the fifth wicket.
Latham again was reliable, making 31 from 53 balls while Foxcroft made 22 from 28.
Left-arm wrist spinner Vitel Lawes put some pressure on the Kiwis with three early wickets but the target was too small to maintain that pressure.
West Indies lost eight wickets in just over 20 overs in the face of excellent spin bowling from left-armer Jayden Lennox who took 4-52 to go with his 5-19 in the second match of the series. Mitchell Santner took 2-15 from 8.1 overs and Michael Bracewell 2-33 on another turning pitch at Providence Stadium.
Lennox has been player of the match in the last two internationals. All of his nine wickets have been bowled or lbw.
"There's obviously no secret to it, it's keep the stumps in play," Lennox said in a post-match television interview. "You have to let the pitch do what it does.
"We can't control that but if we put the ball in the right area we're obviously going to get some rewards."
Things began to go awry for the Windies when opener John Campbell was carried from the field on a stretcher in the sixth over after tearing a hamstring while running between wickets.
They were 0-25 at that point and 1-38 when Campbell's opening partner Ackeem Auguste was brilliantly caught by Santner off the bowling of Jacob Duffy to provide a rare wicket for the seamers.
Lennox bowled West Indies captain Shai Hope (8) and Santner removed Sherfane Rutherford (4). Keacy Carty loomed as a danger to New Zealand, making 48 from 77 balls before being trapped lbw by Bracewell.
When he was out the total was 4-121 but the last five West Indies wickets fell for 19 runs and Campbell was unable to return and resume his innings.
"It's always challenging batting first in Guyana," Hope said. "I'm not being a good captain when it comes to winning the toss.
"I still felt they bowled really well but we have to find ways to score in these challenging conditions."
The series now moves to Bridgetown, Barbados where the fourth international will be played on Sunday.
6°C