The home side’s hopes of chasing down Sri Lanka’s 290-8 nosedived when they crumbled to 21-5 at Eden Park, before being dismissed for 150 off 29.4 overs.
Sri Lanka rebounded after suffering heavy defeats in the first two games to cede the three-match series.
They were led by some lethal seam bowling from Asitha Fernando and Eshan Malinga, who claimed three wickets each, as did spinner Maheesh Theekshana.
Fernando (3-26) was the chief destroyer with the new ball as New Zealand’s first five wickets tumbled inside the first seven overs.
The victory margin would have been greater, were it not for Mark Chapman’s 81 off 81 balls, the number three New Zealand batsman the last out when he was bowled by Theekshana (3-35).
No other New Zealander reached 20, with five of the top six dismissed for two runs or less.
Earlier, injured opener Pathum Nissanka top-scored for Sri Lanka with 66 off 42 balls.
Nissanka, was on 50 off 31 balls when he retired hurt after suffering an apparent hip injury, having got his team off to a flying start at 66 without loss in 10 overs.
He recovered and returned in the 34th over to add a further 16 runs, hitting six fours and five sixes in total.
There were half-centuries from Kusal Mendis (54 off 48) and Janith Liyanage (53 off 52) in a vastly improved Sri Lankan batting effort.
New Zealand seamer Matt Henry continued a fine series, claiming 4-55 to lift him to 150 ODI wickets, while captain Mitchell Santner took 2-55 with his spin.
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