Police said the driver of the 208 was taken to hospital for treatment, and injuries are not thought to be life threatening.
The A19 southbound was closed for over 10 hours, before reopening at around 11am, according to National Highways.
A force spokesperson said: “The 31-year-old driver of the Audi was arrested on suspicion of dangerous driving and drug driving and is in police custody.
“Three other men, aged 37, 34, and 22, who were passengers in the car were also arrested in connection with the incident.
“A 39-year-old man, who was also a passenger in the vehicle has been taken to hospital with non-life-threatening leg injuries.
“A referral will be made to the Independent Office for Police Conduct due to the collision happening after a police pursuit, which is mandatory.”
Anyone who witnessed the black Audi or who may have footage of the incident is asked to contact police through the report section of the Cleveland Police website or by calling 101.