Soak wood chips in a bowl of water, 8 hours to overnight.
Mix paprika, white sugar, cumin, cayenne pepper, brown sugar, chili powder, garlic powder, onion powder, salt, and black pepper together in a bowl. Rub the spice mixture over the entire brisket; refrigerate for 24 hours.
Preheat smoker to between 220 degrees F (104 degrees C) and 230 degrees F (110 degrees C). Drain wood chips and place in the smoker.
Smoke brisket in the preheated smoker until it has an internal temperature of 165 degrees F (74 degrees C), about 12 1/2 hours. Wrap brisket tightly in butcher paper or heavy-duty aluminum foil and return to smoker.
Continue smoking brisket until an internal temperature of 185 degrees F (85 degrees C) is reached, about 1 hour more. Editor's Note: The nutrition data for this recipe includes the full amount of the spice rub ingredients. The actual amount consumed will vary.