Unless the alt is malfunctioning too. The full wave bridge rectifier circuit (voltage regulator) diodes in the alternator can die one by one, as they die, the alternator will give power, but not good usable DC power that the vehicle needs. So your alt can limp along apparently OK enough to charge the battery, keep the vehicle running etc, until the third diode blows then you wont have jack for usable DC power.

If the rectifier circuit is otherwise damaged, and functioning intermittently that can also cause probs like this. Easy fix is to check the battery/cables and terminals as previously mentioned. Then check your alternator. You may find that the alt has blown a couple diodes. Or that they are functioning intermittently. Either way, the fix for that is to replace the alternator as the rectifier circuit (voltage regulator) is built into the alternator and not considered a replaceable part in most modern vehicles.