The parasympathetic system is less important to the Heart than the sympathetic system because not involved as much in reflex feedback. It has no equivalent to the sympathetic’s adrenal medulla epinephrine general body stress effect. The tenth Cranial Nerve (CN X), whose branches supply the parasympathetic nerves to the heart is called the Vagus nerve, and has lent its name to the parasympathetic effect (vagotonic or vagal = HR and BP decrease).
The opioid drugs (morphine et al.) have parasympathetic effect (narrowed pinpoint eye pupils, mild slowing breathing and bronchi narrowing).