But, the men from the Caribbean were spurred on by five wickets from seamer Kemar Roach, who finished the innings with 5-60 - his third-best figures in test cricket, while spinner Sunil Narine chipped in with 3-91.
Narine, who claimed 8-223 in the test, was named man of the match and his first-innings five-wicket haul set the tone for the West Indies who were on top during the contest from day two.
New Zealand's hopes on the final day rested on the shoulders of skipper Ross Taylor and recognised batsmen Kane Williamson, Dean Brownlie and Daniel Vettori.
Taylor started the first session on 11, but only added 10 runs to his overnight total when he was trapped in front by Roach.
Williamson, who courageously made a match-saving century against South Africa in March, wasn't able to repeat his heroics when he was bowled by Roach without troubling the scorers.
Night watchman Wagner, who was on test debut, watched two senior batsmen lose their wicket at the other end, while the South African-born seamer toiled away at the other.
His lengthy vigil of resistance was eventually ended when he was caught behind from the bowling of Roach for 13, but more importantly he batted for two hours and three minutes and chewed up 103 balls.
When Wagner departed New Zealand were in trouble with the scoreboard reading 225-6 with the slender lead of 54 and Brownlie was also sent back to the pavilion on the same total.
Brownlie only managed scores of 23 and five in the test and his place in the side could be under pressure from BJ Watling or coach John Wright may elect to play another bowler at the right-hander's expense.
Vettori, Kruger van Wyk, Doug Bracewell and Chris Martin all came and went with only van Wyk putting up any major fight as he made 30 from 42 balls but New Zealand were eventually bowled out for 272.
Needing only 102 for victory, West Indies openers Chris Gayle and Kieran Powell went about scoring the runs in near-record fashion.
A 10-wicket victory looked on the cards for the Calypso Kings at one point, but Bracewell was able to dislodge Powell for 30.
Gayle made sure no further inroads were made by the Kiwis though as he plundered 64 from 49 balls, including eight fours and two sixes as the West Indies reached the target in 19.3 overs.
The second test starts in Jamaica on Friday.
