Final answer:
The parasympathetic nervous system, part of the autonomic nervous system, directly controls the digestive system by regulating restful processes like digestion and interacting with the enteric nervous system within the digestive tract.
Step-by-step explanation:
The part of the nervous system that directly controls the digestive system is the parasympathetic nervous system. This division is responsible for regulating the body's restful processes, including digestion. It operates alongside the sympthetic division as part of the larger autonomic nervous system, which controls involuntary bodily functions. Specifically, the parasympathetic nervous system slows the heart rate, increases digestive activity, and helps the body to conserve and restore energy.
Within the digestive system, the enteric nervous system, a part of the peripheral nervous system, contains networks of neurons embedded in the walls of the digestive tract. These networks, such as the myenteric plexuses, can directly influence digestive function.