Trim fat from steak. Place steak in a large heavy-duty, zip-top plastic bag. Combine brown sugar and next 4 ingredients; pour over steak. Seal bag; turn bag to coat steak. Marinate in refrigerator 8 hours, turning bag occasionally.
Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Remove steak from marinade, discarding marinade. Place steak on rack; grill, covered, 6 to 8 minutes on each side or to desired degree of doneness. Let steak stand 5 minutes. Cut diagonally across grain into thin slices.