Mr Brosnan and his wife Cherie ran outside to find the car with the engine still running, smoke billowing from the bonnet but the driver gone.
"We just saw a cop run down the stairs and chase him around the side of the house."
The couple grabbed a fire extinguisher for the car before more police, two fire trucks and an ambulance arrived.
Mr Brosnan said they were lucky the car had crashed through the wooden fence and into a concrete wall, stopping it short from plummeting through their guest room wall.
"I was shaken up for a bit," Mrs Brosnan said of the ordeal.
Police spread around the area, parking in surrounding streets to form a loose cordon. Police dog units were also called to the scene.
Local residents stood outside their homes watching the drama unfold.
Police were still searching for the man when the Bay of Plenty Times went to print.