Final answer:
The Facial nerve (CN VII) innervates the orbicularis oculi muscle, which is responsible for closing the eyelids.
Step-by-step explanation:
The cranial nerve that innervates the orbicularis oculi muscle, which facilitates eyelid closing, is the Facial nerve (CN VII). This is part of the corneal reflex, or the eye blink reflex, where the sensory component might travel through the trigeminal nerve (which carries somatosensory information from the face) or through the optic nerve (if stimulated by bright light). The motor response is carried out through the Facial nerve, activating the orbicularis oculi muscle to initiate blinking.