At around 7.30pm, police attempted to pull over a white Citroen at the junction of Beaver Hill Road and Market Street to advise them to turn on their headlights.
The Citroen failed to stop for police and drove off down Beighton Road in the direction of the A57.
Attempting to overtake a vehicle on the opposite side of the road, the Citroen then collided with a red Peugeot.
The driver of the Peugeot suffered minor injuries in the collision.
The driver of the Citroen suffered serious injuries and was taken to hospital to receive treatment.
A South Yorkshire Police spokesperson said: “Enquiries are ongoing, but police would like to speak to anyone who might have seen what happened.”
Call the force on 101, quoting incident number 923 of October 30.