Cook first 3 ingredients in a large skillet over medium heat, stirring until beef crumbles and is no longer pink; drain and return to skillet.
Stir in tomatoes and next 7 ingredients; bring to a boil. Reduce heat, and simmer, stirring occasionally, 20 minutes. Stir in rotini and cheese. Spoon into a lightly greased 13- x 9-inch baking dish.
Bake at 350° for 35 minutes.