Will Young followed up a brilliant team effort in the field with an assured, unbeaten knock of 90 as the Black Caps cruised to a nine-wicket victory.
They took full advantage of skipper Mitchell Santner's decision to put the tourists into bat in conditions favouring seam bowling, with a nasty southerly causing discomfort to players and spectators.
Matt Henry and Jacob Duffy struck early for the Black Caps, and then Santner ran out Kamindu Mendis with a sharp piece of fielding,
At the end of 10 overs, the tourists were 23 for four, with opener Avishka Fernando their big hope.
He batted superbly in the conditions, combining with Janith Liyanage in an 87 run partnership that was the bedrock of their innings.
Henry finished with four for 19 off his 10 overs, while Duffy took two for 39 off 8.4 overs. Nathan Smith chimed in with two for 43, while Santner was tight with his spinners taking one wickets for 27 off his seven overs.
The New Zealanders were able to avoid the early innings horrors experienced by Sri Lanka, with Young and Rachin Ravindra combining in a 93-run partnership before Ravindra mistimed one and was caught on 45.
Young continued on, seldom looking troubled, and one memorable shot was a leg glance for four despite falling to the turf.
He had a good foil in Mark Chapman, who was unbeaten on 29 when Young hit the winning runs.
The second match is at Hamilton on Wednesday.
