At the couple's sentencing in the High Court at Auckland yesterday, Justice Rhys Harrison said that "little fright" was the father's attempts to downplay the moment he inflicted the fatal head injury.
The "deliberate and brutal" blow left her comatose, with her skull fractured and retina detached. She was also malnourished and had a broken leg caused by "deliberate yanking".
Azees Mahomed was sentenced to life in jail for her murder and will have to serve at least 17 years before he's eligible for parole. On three other charges - two of causing the baby grievous bodily harm and one of failing to provide the necessaries of life - he was ordered to serve five years jail on each charge, to be served concurrently with the life sentence.
Tabbasum Mahomed was jailed for four years for failing to provide the necessaries of life after Justice Harrison told her the offending was at the worst end of the scale.
She was not charged with murder.
"Each of you separately denied any knowledge of these injuries," Justice Harrison said. "I was in no doubt it was an extension of the line you two fabricated immediately after the death.
"It was a weak and cowardly strategy and it failed," he said.
The judge said the parents viewed Tahani as a nuisance that got in the way of them building their business selling jewellery at local markets.
Tabbasum Mahomed will be deported back to South Africa when she is released from jail and and authorities there would determine if she will ever be allowed custody of her older daughter.