Sri Lanka's debutant spinner Akila Dananjaya, who was the youngest from his country to play in Twenty20 international, made a memorable debut bagging two for 32 while pacer Nuwan Kulasekara also got two for 33.
While chasing, former captain Tillekaratne Dilshan tore apart the New Zealand bowling with his 53-ball 76 that was studded with five fours and three sixes.
The 80-run opening stand between Dilshan and skipper Mahela Jayawardene (44) kept Sri Lanka on course. But the chase faltered only to see both the teams tied at 174 before the Super Over broke the deadlock.
In Image: New Zealand's wicketkeeper Brendon McCullum, left, watches Sri Lanka's batsman Tillakaratne Dilshan play a shot