They reached their 189-run target in the morning of the fourth day with Kane Williamson not out 108. For Sri Lanka, Dushmantha Chameera took four for 68.
New Zealand won the first Test in Dunedin by 122 runs.
New Zealand beat Sri Lanka by five wickets in the second Test in Hamilton on Monday to wrap up the series 2-0.
They reached their 189-run target in the morning of the fourth day with Kane Williamson not out 108. For Sri Lanka, Dushmantha Chameera took four for 68.
New Zealand won the first Test in Dunedin by 122 runs.