Sri Lanka's task was always uphill. They needed 390 to win and square the series, but having started the day at 45 for one, lost four wickets before lunch, including the key men, Kumar Sangakkara and captain Angelo Mathews for five and eight respectively.
Captain Kaushal Silva made his seventh half century but was a lone performer in the morning session.
Offspinner Mark Craig enjoyed himself after lunch, removing Prasanna Jayawardene, Dinesh Chandimal and Rangana Herath in quick time, at one point sitting on a hat-trick.
Lahiru Thirimanne played some handsome strokes in his best score of the series, finishing 62 not out.
Tim Southee wrapped it up with his only wicket of trhe innings, bowling last man Nuwan Prdep. Craig finished with four for 53, while Doug Bracewell and Trent Boult took two wickets each.
New Zealand have now won four and drawn two of their last six test series.
They now break from test cricket to prepare for the World Cup, starting in New Zealand and Australia on February 14. Their next test assignment is two matches in England in May.
