Only surefire way: Get a chin strap (or fashion yourself one out of a cloth women's headband or other fabric.) These types of Amazon listings boast that the chin strap will stop you from snoring but that's just hype, if you actually snore the best treatment is CPAP (or losing weight, which is free!)
Likely causes of dry mouth: You're physically dehydrated, so drink more water during the day (since you don't want to drink a bunch right before bed.) You could also consider a small external humidifier for your bedroom. There's a small possibility you have clinical dry mouth issues due to an under production of saliva from your saliva glands, in which case you can get moisturizing mouth spray.