Derringer Seth Clarke used both hands to shove 86-year-old Patricia Linburg on December 31, 2018, causing her to fall over and break a femur bone.
She required hospitalisation and surgery, but her condition deteriorated and she died on January 6.
Clarke was initially charged with manslaughter before this was changed to causing grievous bodily harm with reckless disregard for the victim's safety.
He then pleaded guilty.
Justice Mathew Downs in the High Court at Hamilton subsequently sentenced Clarke to six months' home detention today, saying he was satisfied prison "would be the wrong response".
"The point I wish to emphasise is this: you have been fortunate today. You will not get a second chance," Downs said.
Justice Downs earlier described the facts of the attack as simple but distressing.
Clarke had been living in a garage in the family home when on the morning of December 31, he was on a ramp that led to the kitchen.
Lindburg, who was the mother of Clarke's stepfather, then confronted him because he was not allowed inside the house.
"She told you repeatedly to leave," Justice Downs said during the sentencing.
"You did not. You belittled her. Mrs Linburg attempted to remove you by pushing and 'hitting out'," he said.
"You then pushed Mrs Linburg to the chest with both hands. In short, you shoved her."
Lindburg fell to the kitchen floor, breaking her leg and later dying in hospital
Justice Downs said that as Clarke had not been charged with manslaughter, he was not criminally responsible for Lindburg's death. Therefore, he was simply being sentenced for shoving Lindburg to the ground.
Justice Downs did not accept Clarke had shown enough remorse to be given a discount in his sentence and also did not accept claims by his lawyers that his "dysfunctional family background" deserved leniency.
However, with Clarke being 20 years old he did accept there was a good chance for his rehabilitation and that prison could be a hindrance to this.
This was a sentiment accepted by Lindburg's family and prosecutors, Down said.
He also said the level of violence used by Clarke was less than that typically seen for a charge of causing grievous bodily harm.
"To be clear, your violence was serious. My point is that it is less serious than is often the case when this offence is charged," he said.
He also gave Clarke a first strike warning, meaning he would not be eligible for parole or early release if he was convicted of any more serious violent offences other than murder.
If convicted of murder he would be sentenced to life imprisonment without parole unless this would be "manifestly unjust".
