The police Eagle helicopter relayed information to officers on the ground, Inspector Mark Chivers said.
The children allegedly hit the pedestrian in Manurewa, Chivers said. The pedestrian was unharmed.
The group then stopped on Seaward Place in Wattle Downs, where three passengers got out and continued fleeing on foot.
The remaining children in the car then drove to Burbank Ave in Manurewa, where they got out and ran into a property.
Police arrested all the children without further incident, Chivers said.
He said: “It is incredibly fortunate no one was seriously injured as a result of this incident.”
Police referred the children to Youth Aid Services.