Scorecard
The Kiwis, who won the first match on Wednesday by three runs, piled up 170-4 after winning the toss and then restricted the World Twenty20 finalists to 148-8 under lights at the Premadasa stadium.
Fast bowler Shane Bond led the Black Caps charge with 3-18 in four overs, while seamer Kyle Mills and off-spinner Nathan McCullum claimed two wickets each.
The 2-0 win helped the Kiwis overcome the disappointment of losing both the preceding Test matches and boosted their confidence ahead of a tri-series, also featuring India, that opens on Tuesday.
New Zealand's innings revolved around an explosive opening stand of 84 in 10.2 overs by Brendon McCullum and Jesse Ryder after Vettori called correctly for the second time in a row.
Left-handed Ryder smashed three sixes and as many fours in his 52 off 37 balls, while McCullum hit a 34-ball 49 with two sixes and four boundaries.
Martin Guptill and Jacob Oram further boosted the total with a 43-run stand for the fourth wicket in 27 balls, before Guptill was bowled by Lasith Malinga off the final ball of the innings.
Sri Lanka, chasing a target of almost nine runs an over, made a disastrous start when they were reduced to 2-2 off the first seven deliveries and slid to 11-3 soon after.
Bond removed the in-form Tillakaratne Dilshan with his fifth ball, caught at deep square leg, before Kyle Mills dismissed Mahela Udawatte and Sanath Jayasuriya in successive overs.
Skipper Kumar Sangakkara and former captain Mahela Jayawardene put on a brisk 67 for the fourth wicket when Nathan McCullum hit back with two wickets in his first over.
The off-spinner, elder brother of Brendon McCullum had Jayawardene caught at backward point by Ryder off his third delivery for 41 off 30 balls.
He then removed new batsman Angelo Mathews with the final delivery of the innings to make Sri Lanka 80-5 in 11 overs.
Sangakkara gave Jacob Oram a return catch after making 69 before Bond sealed New Zealand's win with the wickets of all-rounder Gihan Rupasinghe and tailender Nuwan Kulasekara.
Earlier, McCullum and Ryder bulldozed the Sri Lankan attack for the first 10 overs, racing to 83 runs without being separated.
Jayasuriya broke the stand in the 11th over when he beat McCullum in the air and the batsman offered a simple return catch.
Ryder took over after McCullum's departure, striking two sixes and a boundary in the 12th over sent down by Dilshan which yielded 20 runs.
Jayasuriya finished with 2-22 and Ajantha Mendis took 1-21, while pace spearhead Kulasekara went for 40 runs in four wicketless overs.
