Hawke's Bay Today understands the driver fled on foot, before being arrested nearby.
Foster said his staff rang the bell immediately, putting the school into voluntary lockdown as a precaution.
He then rang police to tell them what he'd done and that the children were safe in their classrooms.
"It was really lucky that our morning tea had finished, otherwise things could have been different," Foster said.
"It's just stupid that someone thought it was a good idea to use school grounds as a way to try to escape police."
A police spokeswoman said two people were now in custody.
The chase began about 11.40am when a suspicious vehicle was seen in the Maraenui area and failed to stop for police when signalled.
Two schools, Richmond and Bette Christie Kindergarten, went into a voluntary lockdown as a precautionary measure but stood it down after an hour.
Police said searches on foot around the Maraenui suburb later located the alleged offender nearby. They were taken into custody without further incident.
The person is expected to face various charges and is due to appear in court tomorrow. Another person was arrested for obstruction.
"Police would like to thank the schools and the public for their patience while police dealt with this unfolding incident."
In December, Flaxmere Primary School placed itself in lockdown after a man came on to the school grounds, and was shot by police.
Derek Timu, who was known to a school staff member, survived the shooting and has pleaded guilty to several charges including unlawfully carrying an imitation firearm.
He will be sentenced next month.
