Chasing 158 for victory in Hamilton, New Zealand overcame a wobbly start that saw them lose two wickets in the second over and got home with 103 balls to spare thanks to an unbeaten 86 by batsman Will Young and a 44 not out by Henry Nicholls.
Sri Lanka chose to bat first after winning the toss but only opening batsman Pathum Nissanka (57), skipper Dasun Shanaka (31) and Chamika Karunaratne (24) made notable scores as Matt Henry, Henry Shipley and Daryl Mitchell bagged three wickets each.
India and six other teams have booked their spots in the World Cup starting in October, with the West Indies occupying the final automatic qualification place in the Super League standings. South Africa and Ireland are also in contention.
Sri Lanka will now look to earn their berth via a 10-team qualifying competition in Zimbabwe in June and July.
The 1996 world champions received five points following the abandoned second ODI rather than the 10 a win would have offered and were also docked a point for maintaining a slow over-rate during their 198-run defeat in the opener.
New Zealand also won the preceding test series 2-0 to dash Sri Lanka's hopes of reaching the World Test Championship final. They next host them in three Twenty20 Internationals, with the first match in Auckland on Sunday.
