An autonomous drilling pressure control system for use with a drilling rig includes a pressure control device for controlling pressure within an annulus of an associated well, an electronic pressure sensor for monitoring pressure within the annulus, and an electronic position indicator for indicating a position of the pressure control device. A control subsystem independent of the drilling rig and responsive to the pressure sensor is provided for manipulating the pressure control device to control the pressure within the annulus of the associated well. At least one dedicated power source independent of the drilling rig supplies power to the pressure sensor and position indicator.