Final answer:
The glossopharyngeal nerve (cranial nerve IX) is responsible for connecting to the taste buds in the posterior part of the tongue, conveying taste sensations to the brain and stimulating saliva production.
Step-by-step explanation:
The cranial nerve that serves the posterior taste bud-containing parts of the tongue is the cranial nerve IX (Glossopharyngeal nerve). The glossopharyngeal nerve connects to taste buds in the posterior two-thirds of the tongue and is responsible for the sense of taste, as well as causing saliva production. It also conveys gustatory stimulation to the brain, playing a critical role in the sensory pathway for gustation.