Batting first the Black Caps recovered from a slow start before Mark Chapman (76 from 81) and Mitchell Hay (49 from 66) put on 75 for the fifth wicket.
However, the Black Caps lost their final six wickets for 34 runs to be bowled out for 209 in 45.1 overs. Theekshana (3-31) was the pick of the Sri Lanka bowlers.
“It is always a challenge when you are defending a low score,” Black Caps skipper Mitchell Santner said.
“Kusal played the situation very well. We were trying to get the run-rate up but it never got over five. That partnership at the end took it away.”
“Good performance with the ball to squeeze them and take wickets. We got a lot of spin in, was surprised it spun that much in the night. If we put up a few more runs out there and got to 240, it might have been a different story,” he added.
Being sent into bat, New Zealand lost opener Tim Robinson in the second over when he was bowled by Dunith Wellalage for four. Henry Nicholls joined him six overs later after he was also bowled, castled by Maheesh Theekshana for eight off 23 balls.
That left New Zealand 31-2 from eight overs before Will Young and Chapman appeared to get the innings back on track. Young was stumped off the bowling of Jeffrey Vandersay (who finished with 3-46) for 26 and when Glenn Phillips (15 off 22) followed him seven overs later New Zealand were 98 for four at the midway point.
Chapman and Hay upped the run rate and got the Black Caps through to 173 for six, setting a platform for the final 10 overs before the innings collapsed.
The final ODI takes place on Tuesday night.
The Alternative Commentary Collective is covering every home Black Caps this summer. Listen to live commentary here.