Police said an officer was responding to an emergency call at 19:00 BST when the car collided with a Ford Fiesta and hit a lamp-post on Park Road, Toxteth.
The police officer was taken to hospital with a back injury. The occupants of the Fiesta were assessed by paramedics at the scene.
An investigation into the circumstances of the collision is under way.
Two 14-year-old boys from Aigburth have been arrested on suspicion of attempted robbery in relation to the original 999 call.
A police car flipped on its side as it went to the scene of an attempted robbery last night in Liverpool.