A nephew who lived in the house had shouted for the driver to "watch out" but the driver could not hear "because the windows were up".
After the accident, Miss Salesa said she saw the man shouting for his wife, who appeared shocked .
He had asked her to hold the child but she could not carry the girl into the house, she said.
"I went to their house and saw the [man] sitting on the table and holding on to the baby ... he didn't let her go until the ambulance arrived."
The Herald understands the couple have an older son and were sharing the two-bedroom unit with another couple and their nephew.
Miss Salesa, who did not know the names of her neighbours, said up to six or seven people could be living in the rear unit on Massey Rd in Mangere.
No one was at home when the Herald visited the house yesterday.
Police would not confirm who the driver of the vehicle was, but said it was "a person close to the child".
"[The] parents were spoken to briefly following the crash, however the investigation is in its early stages and there are a number of formal statements yet to be taken," said police spokeswoman Kimberley Mathews.
"The parents will be given some time to support their daughter in hospital."
Ms Mathews said it was too soon to know if charges would be laid.
The toddler remains in a critical but stable condition in Starship children's hospital.
Studies by Safekids Aotearoa found driveway runovers occurred more frequently where families were higher than average size and population densities were high.
"Every two weeks a child is hospitalised with serious injuries received from a vehicle driving on a private driveway in New Zealand," said Ann Weaver, Safekids director.
"A further five children are killed annually, on average, in the same way."
This was the fourth time a child had been run over in the past eight months.
Ms Weaver said most children killed or injured were toddlers and the driver was usually the father, mother or a close family member.
Two weeks ago, 3-year-old Valentina Grace Warren was killed by a vehicle in the driveway of her Te Atatu, West Auckland.
In March, toddler Mila Tamihana was found in her Cartmel Ave driveway in Massey with fatal injuries after being hit by a car. Te Manawa Whetuki Renata, 23 months, died after being hit by a vehicle in his Papatoetoe, South Auckland driveway in April.
Driveway toddler toll
killed each year: 5
hospitalised with serious injuries each month: 2
children have been run over in the past 8 months: 4
average age of victims: 2
(Source: Safekids Aotearoa)