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.