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.  

the oxygenated blood then leaves the lungs through pulmonary veins, which return it to the left heart, completing the pulmonary cycle. this blood then enters the left atrium, which pumps it through the mitral valve into the left ventricle. from the left ventricle, the blood passes through the aortic valve to the aorta.

deoxygenated blood leaves through the right ventricle through the pulmonary artery. from the right atrium, the blood is pumped through the tricuspid valve (or right atrioventricular valve), into the right ventricle.