Elliott had taken the car, which belonged to a friend, without asking.
The court heard victim impact statements from Shaun's family including his parents Brett and Tina who said their only son's death had shattered their lives.
They had already suffered the loss of a daughter 12 years earlier and now, their youngest and only surviving child, five-year-old Laura, was also devastated by the loss of her brother.
"I miss my son terribly," Mrs Nilson said.
"I cry every day... I spent many years after the loss of my second born learning to fully love again without fear and without holding back so I wouldn't have to feel that pain again. I must now endure that all over again after my first born and my only boy was killed."
Justice Ellis sentenced Elliott to three years without a minimum term and disqualified him from driving for four years from his release.
She took into account Elliott's guilty plea, age, remorse, good character and sporting achievements including being a representative softball player, in determining the sentence.
She said Elliott would be imprisoned in a facility where he was not exposed to hardened criminals or gang members but the teenager's family were visibly distressed at the prison sentence.
In a statement to media Elliott said he was "very sorry for the pain, loss and suffering" he had caused the Nilson family and there were no words which could make right the situation.
He was granted bail to begin his sentence on Monday so that he could attend his grandmother's funeral in Otorohanga tomorrow.