Which cranial nerve innervates several different systems including blood pressure, digestion, and cardiac rhythm?

Vagus nerve.

Explanation:

Vagus nerve is the tenth cranial nerve and largest among all the cranial nerves. This nerve transmits information to or from the surface of brain to the tissue or organ.

Vagus nerve is responsible for regulation of various functions like sweating, blood pressure, digestion, peristalsis and cardiac rhythmicity. Cranial nerve innervates in different system of body like digestion, blood pressure and cardiac rhythm.