The hosts won all three matches in this rain-hit series under the Duckworth/Lewis method.
New Zealand captain Ross Taylor won the toss and asked Sri Lanka to bat first, and they slumped to 123 for eight when rain stopped play.
Upul Tharanga scored 60 runs for Sri Lanka and seam bowler Tim Southee took three wickets for New Zealand.
Sri Lanka captain Mahela Jayawardene said that his team did what it needed to in the crucial moments of the series.
"The guys were pretty down after the T20 World Cup, and everyone did a tremendous job in lifting themselves up," he said.
Taylor said his team improved along the way even though they lost the series.
"We need to work on all three facets of the game," he said. "We made some improvements and we need to get better to repay our fans back home. Today's a good start."
Having already clinched the series, Sri Lanka looked to experiment by giving its young batsmen a chance to bat up the order. But the youngsters failed.
Opener Dinesh Chandimal was bowled by Southee for a first-ball duck with the total just three. The delivery shaped in and seamed away to hit Chandimal's off stump.
Lahiru Thirimanne was promoted to No. 3 and got a promising start playing three well-timed drives for boundaries in his 17 runs off 15 deliveries. He was out caught by wicketkeeper Bradly-John Watling trying to chase a wide delivery from Southee.
Thirimanne and Tharanga shared 30 runs for the second wicket but failed to build on that platform.
Angelo Mathews was also out without scoring when he top-edged a pull shot for a catch to Southee in the deep off seam bowler Trent Boult.
Adam Milne picked up the prized wicket of Kumar Sangakkara for his maiden one-day international dismissal to leave Sri Lanka four down for 44.
Tharanga and Jayawardene tried to steady the innings with a 47-run partnership for the fifth wicket but Jayawardene (24) was run out to a brilliant direct hit from Nathan McCullum.
Rain came down as Tharanga was out also caught by Watling for Southee's third dismissal. Tharanga faced 94 deliveries and hit eight boundaries.
Southee had best figures 3-18 while seamer Andrew Ellis returned 2-22.
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