Check the output voltage from your alternator. It should be around 13.5 to 14.3 volts. (you should be able to do this with a basic multi meter or bring it to a local auto parts store that offers free diagnosis)The symptom your describing sounds like a charging issue. Most all components are designed to run off a full 12 volts. If it falls below that, it can affect the engine idle circuit.
It is similar to jump starting another car that has a dead/weak battery. Once the cables are connected, you will notice the engine in the car delivering the charge decrease RPM's to compensate the load.