Herings nerve. Vagus doesn't play a big role here.
Actually, in cases of vaso-vagal syncope it does (hence, the "vagal"). The branch of the glossopharyngeal nerve to the carotid sinus ("Hering's nerve") carries the signals from the baroreceptors to the brainstem. If the baroreceptors sense increased blood pressure, a signal is sent from the brainstem via the vagus nerve to activate the parasympathetic nervous system to slow the heart (bradycardia).
Also, it would be good to resurrect this gem: