Final answer:
The enteric nervous system, part of the peripheral nervous system and functioning with the autonomic nervous system, directly controls the digestive system.
Step-by-step explanation:
The part of the nervous system that directly controls the digestive system is the enteric nervous system, which can be considered as part of the broader autonomic nervous system. The autonomic nervous system is divided into the sympathetic and parasympathetic nervous systems. While the sympathetic nervous system is associated with the fight-or-flight response, the parasympathetic nervous system largely influences rest-and-digest functions, and therefore, helps to control digestion. However, the enteric nervous system is more directly responsible for regulating digestive processes as it operates within the digestive organs themselves. It is a subset of the peripheral nervous system (PNS), functioning independently from the central nervous system (CNS), though it often interacts with the autonomic nervous system for coordinated responses.