The suspect, identified as 22-year-old Calvin Felder, slammed into an SUV in Deer Park just after 1 a.m.
A passenger in the car, 22-year-old Mark Smith, was taken to the hospital in critical condition.
Felder and the driver of the SUV, 39-year-old William Keyser, both suffered non-life-threatening injuries.
The chase started when police tried to pull over the suspect in Bay Shore.
The driver is under arrest, charged with driving while ability impaired by drugs and unlawfully fleeing a police officer.