Ireland were bowled out for 232 in the second innings just before tea on day three of the four-day Test.
Blair Tickner starred with his first Test five-for, 5-76, in his fifth match. Fellow seamer Nathan Smith started the day with five maidens and took 2-53 and eight wickets in the match.
"We like coming over to this part of the world," skipper Tom Latham said when asked about their confidence going into the three Tests with England starting next Thursday at Lord's.
"We have a good opportunity to put our best foot forward, play our brand of cricket, and if we do that we know we will give ourselves a good chance."
In reply to New Zealand's 8-490 declared, Ireland were dismissed for 179 on Thursday and forced to follow on, and began the day at 2-65 with a target of 312.
A team with three debutants, missing their best player Paul Stirling, and playing their first home Test in nearly two years were always struggling against New Zealand's pace attack.
Nightwatchman Thomas Mayes lasted only five overs then Tickner got Harry Tector to edge to second slip.
Stephen Doheny, 36 overnight, reached his maiden test fifty off 96 balls. Then Curtis Campher retired hurt with a suspected broken left hand hit by a Ben Sears delivery.
A Tickner snorter prised out Doheny for 57 and Ireland were 5-131 but effectively six wickets down when lunch was taken a few minutes early because of drizzle.
Ireland scored only 66 runs in 29.1 overs in the morning session and lost four wickets.
Lorcan Tucker counterattacked for his fourth test fifty off 69 balls then was out next ball to a Smith bouncer, and the end came quickly to the only Test of Ireland's summer.
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