New Zealand posted a score of 174-7 to keep the match competitive, with opener Rob Nicol top-scoring on 58 runs.
Sri Lanka started their reply strongly before Mahela Jayawardene was dismissed by Jacob Oram for 44.
The hosts needed eight runs from the final over to claim victory, and the battle went right down to the final ball.
With the scores level and one ball left to play, a video review was required to decide the winner. After a long delay the umpire decided to send the match to a sudden-death final over.