Police are trying to piece together the incident, which happened at about 7pm.
"The stolen car came through the house and then two police four-wheel drives, pretty much bumper to tail gate," a neighbour has said.
The toddler was immediately rushed to Westmead Children's Hospital in a critical condition where doctors tried frantically to revive her.
A neighbour reported seeing the mother being taken away from the scene, utterly distraught and struggling to keep her head up. The little girl is believed to be a twin and one of eight siblings who are all traumatised by the incident.
The offenders had been described by the police as "violent and a risk to the community", after continuing on and crashing through another fence and then into Richell Park, driving towards fifteen other children playing cricket, who quickly dropped their bats and ran.
Police have launched a critical investigation into the pursuit which Assistant Commissioner Frank Mennilli described as an "absolute tragedy" that had devastated the police officers involved.
"I am overwhelmed for the poor family and what they are going through," he said.
The male driver and a 23-year-old female passenger fled the scene, but the passenger was later arrested by police at Darlinghurst.
The woman was refused bail, to appear before Central Local Court today.
Witnesses said there were no police sirens during the chase.
Assistant Commissioner Frank Mennili said it is not clear whether the offending car, or the police following, hit the toddler. Investigations continue.