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India had surrendered the second position to Kiwis after the humiliating 200-run loss in the series-opener.
Opener Upul Tharanga (70 off 109) was top scorer in Sri Lanka's haphazard chase as Sri Lanka scored 195 for seven in 40.5 overs in a target of 193.
New Zealand, electing to bat, were all out for 192 in 48.1 overs after Sri Lanka's pace duo of Lasith Malinga (3/35) and Angelo Mathews (3/36) shared six wickets between them.
The Kiwi total was built around some good effort by debutant BJ Watling (55) and Nathan McCullum (36).
The low-scoring match at Rangiri Dambulla stadium was a dull affair as only 32 boundaries, including just two sixes, were scored in the flood-lit encounter.
New Zealand, who had 117 rating points before this match, lost three points to slip to fourth spot behind South Africa (115).
India gained a position to second with 116 points behind leaders Australia (132).
Like the Kiwis, Sri Lankan made a wretched start, losing opener Tilakkaratne Dilshan (5) in the third over.
Tharanga raised a 85-run stand for the second wicket with skipper Kumar Sangakkara (48) to steady the innings and then along with Thilan Samaraweera (36 off 38) steered the hosts close to win.
But once Tharanga departed in the 37th over, wickets started tumbling and the hosts were reduced from a comfortable 162 for four to 180 for seven in a gap of 14 balls.
However, seasoned Samaraweera kept his cool and brought his side home with 9.1 overs to spare.
Tharanga's patient knock had nine boundaries and Samaraweera helped himself with four boundaries with last one coming for winning runs off Kyle Mills.
Mills was the highest wicket taker for the Kiwis with outstanding figures of 4 for 41.
Earlier, after a high in the opening match, in which they beat India by a massive 200 runs, the Kiwis hit a low with half of their side returning back to the pavilion inside 23.1 overs.
New Zealand: 192 all out in 48.1 overs (BK Watling 55, Lasith Malinga 3/35, Angelo Methews 3/36, Rangana Herath 2/35).
Sri Lanka: 195/7 in 40.5 overs (Upul Tharanga 70, Kumar Sangakkara 48, Thilan Samaraweera 36 not out; Kyle Mills 4/41).