Police say the white Chevy Malibu with South Carolina license plates came up for motor vehicle violations, but the driver refused to stop.
Instead, the driver continued south on the Turnpike with state police troopers in pursuit. They chased the Malibu across the Goethals Bridge and onto the Staten Island Expressway.
The Malibu got off at Exit 7, but the driver got lost, ending up on a dead-end street. Troopers boxed in the vehicle on Park Drive North, a small cul-de-sac.
Police say the driver attempted to drive through the blocking troopers and their patrol cars. Troopers fired shots at the vehicle to make it stop. No one was hit.
The troopers quickly took the occupants of the Malibu into custody.
The woman who was driving and the man in the passenger seat face charges including assaulting an officer and resisting arrest. Their names were not immediately released.
A couple of state troopers suffered injuries when the Malibu driver tried to barrel through them. They were hit by debris kicked up by the vehicle.
Officials say one sustained a head injury, and another had a hand injury.
They were taken to Staten Island University Hospital North for treatment. Their injuries were described as minor.