Preheat oven to 400°F (200°C); line a large baking sheet with foil and top with a wire rack, or spray foil directly with cooking spray.
Pat drumsticks dry with paper towels for crispy skin.
Toss drumsticks with oil, garlic powder, onion powder, paprika, salt, and pepper in a large bowl to coat evenly.
Arrange on prepared sheet without touching.
Bake 25 minutes; flip drumsticks.
Brush all sides generously with BBQ sauce; bake another 15-20 minutes until chicken reaches 165°F internally and sauce is sticky and caramelized.
Rest 5 minutes; serve with extra BBQ sauce for dipping.