Combine rub ingredients in small bowl; press evenly onto beef brisket. Place brisket, fat side up, in stockpot.
Combine barbecue sauce and wine in small bowl. Pour around brisket; bring to a boil. Reduce heat; cover tightly and simmer 2 1/2 to 3 hours or until brisket is fork-tender. Remove brisket; keep warm.
Skim fat from cooking liquid. Bring cooking liquid to a boil. Reduce heat to medium and cook, uncovered, 8 to 10 minutes or until reduced to 1 cup sauce, stirring occasionally.
Trim fat from brisket. Carve diagonally across the grain into thin slices. Serve with sauce.
Smoker Method Variation: To smoke beef brisket, prepare charcoal or gas smoker according to manufacturer’s directions. Combine barbecue sauce and wine in small saucepan; bring to a boil, stirring frequently. Reduce heat to medium-low; cook 7 to 8 minutes or until reduced to 1 cup, stirring frequently. Reserve 1/2 cup barbecue sauce for serving. Prepare rub as above; press evenly onto beef brisket. Smoke brisket according to manufacturer’s instructions and cooking times or until fork-tender, brushing occasionally with remaining barbecue sauce. Carve brisket as above. Serve with reserved sauce.