Place the roast on a cutting board and liberally coat on all sides with the rub. Using your hands, rub the "rub" into the roast. Place the roast into a large dutch oven and refrigerate, covered, for at least 2 hours.
Preheat oven to 325 degrees F.
Combine liquid ingredients and the garlic powder in a medium bowl and pour into the dutch oven with the roast. Top the dutch oven first with a sheet of foil, tucking it tightly around the rim. Cover with the lid to the dutch oven to form a tight seal.
Roast for 4 hours or until fork tender and shreds easily.
Remove from oven and place on a baking sheet. Allow to rest until cool enough to handle. Shred the pork with a fork or tongs. Serve immediately or refrigerate to use within a couple days.