The Grizzlies repelled wave after wave of attacks in the final 10 to 15 minutes as the Sharks searched for a converted try.
Fullback Joshua Augustine dropped the ball cold with the line wide open and replacement back Benjamin Paku let the pill slip half a metre from the line. All he had to do was catch it and flop over.
Green Island got some good fortune there. But they also created their own luck.They often attacked from their own 22 and scored some cracking tries.
Centre Levi Harmon emerged as one of the heroes.
But there was nothing wrong with his leg when he crashed through two defenders to score midway through the first half.
And there was nothing wrong with it again when he cut in, threw a dummy and cut back out to leave three defenders in his wake and finish off a superb team try early in the second spell.
But Dunedin kept in touch with an intercept try to Kyan Rangitutia, and fellow outside back Tayne Harvey somehow flicked on a pass to hooker Liam Arthur-Hunt who dived over in the corner.
They tried desperately to nab a third but could not find a way through the Green Island wall.