Place the brisket in an aluminum pan. Pour the marinade over it. Cover and refrigerate for 6 hours, or preferably overnight.
Thirty minutes before you are ready to cook the brisket, heat a smoker to 350°F. Alternatively, prepare a charcoal grill for smoking.
Remove the brisket from the marinade and discard the marinade.
Using paper towels or a clean kitchen towel, pat the brisket dry all over. Using your hands, apply the rub all over the meat. Place the brisket in a clean aluminum baking pan, place the plan in the smoker, and cook uncovered for 1 hour.
Remove the pan from the smoker and cover it with aluminum foil. Put it back on the smoker and cook for another 30 to 45 minutes, until the internal temperature registers 205°F.
Remove the pan from the smoker and let the brisket rest, covered, for at least 30 minutes. One hour is preferable.
Remove the brisket from the pan and transfer it to a cutting board, reserving the accumulated pan juices. Using a sharp serrated knife, slice the brisket against the grain in slices about 1/8 to 1/4 inch thick. Try to cut the slices in a consistent size. Place the slices on a warm platter, pour the pan juices over the brisket slices, and serve immediately.