Child Youth and Family (CYF) and the police were notified of the incident as is protocol when a child has unexplained injuries.
Misipati initially said he slipped and dropped the baby in the bath, but police did not believe the injuries, which also included a broken femur and two broken ribs, were accidental.
Eventually, Misipati admitted to hitting the baby, saying he struck him on the top of his head with his knuckles in frustration because the baby would not stop crying or drink from the bottle.
It was the conviction for this offence which led to deportation proceedings, however the Immigration and Protection Tribunal found there was sufficient public interest and exceptional humanitarian justification to allow Misipati to stay in New Zealand with his young family.
Misipati and Ms Silva, have four children together under the age of seven, each of whom the Tribunal considered should have a positive male role model present in their lives.
The Tribunal believed Misipati was capable of becoming that role model.
It particularly took into account Misipati's completion, before beginning his sentence, of an anger management course.
Additionally, Misipati completed the intensive Saili Matagi course while in prison, a culturally focussed program aimed at addressing violent offending, something Ms Silva, said had made a significant difference to his ability to express himself.
The Tribunal considered Misipati has gained insight into his offending which, while serious, appeared to be judged to be at the lower end of the scale.
Risk of re-offending was also deemed to be low.
Misipati said he was open to attending more courses now his sentence had ended and has made promises to his children that he will never hit them again.
It was also taken into consideration the financial hardship Ms Silva would face should Misipati be deported, based on the difficulty she had supporting her family while he was in prison.
Ms Silva said she loved Misipati and it would "break her heart" to have him sent back to Samoa, the Tribunal heard.
The case for Misipati's deportion on the basis of his offending against his child was found by the Tribunal to be outweighed by the benefits to his family for staying.
"There are exceptional circumstances of a humanitarian nature that would make it unjust or unduly harsh for the appellant to be deported from New Zealand," the Tribunal said.
"If the appellant were to remain in New Zealand, he hopes to return to the family home, and to be reunited with his partner and his children, with whom he is closely bonded.
"He maintained contact with them while he was in prison: they visited regularly and he has resumed contact since his release from prison in late April 2015."
Misipati moved in with his sister, who also lives in New Zealand, in June 2013 when the charges against him were laid.
After his release from prison he lived with his family for six days before again living with his sister at the request of CYF.
It was six days until CYF became aware he was back at the family home, and the agency subsequently ensured he moved out.
In response to the incident Corrections Minister Judith Collins will today ask Corrections to change its protocols to ensure it automatically notifies CYF when a person convicted of child abuse is released into the community.
This morning Ms Collins told Radio New Zealand that she would today ask Corrections to look at amending its protocols to ensure CYF were notified of such cases.
"CYFs should be advised if there is someone with a history of child abuse, particularly who has been sent to prison for that child abuse, going back into the community.
"It makes absolute perfect sense for CYF to be automatically advised."
Ms Collins said she did not believe it would be too difficult to make such a change, but if it required a law change she would take that on.
Meanwhile, CYF's South Auckland site manager Anna Palmer said the family had worked cooperatively with the department and believed there were no wider issues of neglect or abuse which needed to be addressed beyond the injuries inflicted to the couple's youngest child.
"CYF therefore aims to facilitate the safe reintegration of the appellant into the family home," she told the Tribunal.
The Tribunal was satisfied the family was working well with CYF to achieve this.
If Misipati is jailed for another offence in the next five years he will be deported.
