drivel, drip, slaver, salivate, spit, water at the mouth, dribble, trickle, ooze, run (out); see also drop 1.
drool over, rhapsodize, lick one's chops*; see want 1.
"drool." YourDictionary, n.d. Web. 16 May 2018. <http://thesaurus.yourdictionary.com/Drool>.
drool. (n.d.). Retrieved May 16th, 2018, from http://thesaurus.yourdictionary.com/Drool
To let saliva run from the mouth:
Saliva running from the mouth: