That meant Sri Lanka won their fifth ODI series at home this year after beating the Black Caps in the first two rain-disrupted games.
New Zealand made its most promising start in the series on Tuesday, reaching 1-112 in 21 overs before rain prevented any further play.
Will Young completed his half-century and was unbeaten on 56 while Henry Nicholls finally got among the runs by scoring 46 not out.
Both batters looked set to post a challenging total as they shared an 88-run stand off 106 balls.
Sri Lanka captain Charith Asalanka timed a leap to perfection at mid-off and took a spectacular catch over his head to dismiss Tim Robinson for nine in the fourth over.
Rain deprived Sri Lanka of testing their bench strength after the hosts made five changes. Seam bowling allrounder Chamindu Wickramasinghe debuted but bowled only two overs for 14 runs.
New Zealand brought in fast bowlers Zakary Foulkes, who made his ODI debut, and Adam Milne in place of Nathan Smith and Jacob Duffy. Milne replaced Lockie Ferguson, who flew home after a calf injury during the preceding drawn Twenty20 series at Dambulla.
The series served as preparation for New Zealand for next year's Champions Trophy which Sri Lanka failed to qualify for after finishing ninth in last year's World Cup in India.
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