Preheat your oven to 425°F (220°C) and line a baking sheet with parchment paper or aluminum foil for easy cleanup.
Pat the drumsticks dry with paper towels. Dry meat browns more evenly and adheres better to the seasoning.
In a small bowl, whisk together olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Toss the drumsticks with the oil-and-spice mixture until they are evenly coated.
Arrange the drumsticks on the prepared sheet in a single layer, giving each piece some space for air to circulate. This helps them crisp while baking.
Bake for 25 minutes, then brush or drizzle with half of the BBQ sauce. Return to the oven and bake for another 5 minutes.
Flip the drumsticks, baste with the remaining BBQ sauce, and bake for an additional 5–8 minutes, until the internal temperature reaches 165°F (74°C) and the glaze is glossy and sticky.
If you like extra glaze, switch to broil for 1–2 minutes at the end, watching closely to prevent burning. Remove from the oven and let rest for 3–5 minutes before serving.
Serve warm with extra BBQ sauce on the side for dipping, and pair with simple sides like corn on the cob, coleslaw, or a green salad.