CHICAGO—Police brass in recent days stripped three officers of their powers in the wake of a fatal shooting of an unarmed black man suspected of stealing a car and fleeing Thursday, an unusually swift response amid intense scrutiny over police action here.

Police followed a Jaguar convertible they suspected was stolen and attempted to pull it over, according to a statement from the police department after the incident Thursday evening. When the driver refused to stop, sideswiping a police vehicle and another car, two officers...