Engine 250 was heading west on Foster Avenue just before 1 p.m., when a Honda coupe heading south on Coney Island Avenue in Flatbush sped up as the fire engine approached the intersection, witnesses said.
The engine hit the rear of the car, sending it spinning across the intersection and into a cable-TV van.
Firefighters used the jaws of life to remove the driver and passenger from the Honda.
Both were taken to Kings County Hospital, where they are in stable condition.