The loss leaves Sri Lanka - champions in 1996 and having played in every previous 50-over showpiece tournament - sitting ninth in the ICC Men's Super League standings with only the top eight qualifying automatically for the finals in India later this year.
After Sri Lanka won the toss and elected to bat, New Zealand's bowlers dominated with Matt Henry, all-rounder Daryl Mitchell and paceman Henry Shipley all taking three wickets as the tourists were dismissed for 157 in the 42nd over with opener Pathum Nissanka making 57.
Although New Zealand lost wickets in their reply at 59 for four, Will Young (86 not out) and Henry Nicholls, unbeaten on 44, combined to help guide them to their victory target in the 33rd over and secure a 2-0 win in the three-match ODI series.
Sri Lanka will now compete along with five Associate teams in the ICC Men's Cricket World Cup qualifier tournament in Zimbabwe during June, when the top two nations will progress to the finals in October.
