Preheat oven to 350°. Brown beef and onions over medium heat in skillet until meat is no longer pink. Add garlic; cook 1 minute longer. Drain. Stir in tomatoes, spaghetti sauce, and mushrooms. Bring to a boil. Reduce heat; simmer uncovered, 20 minutes.

Cook pasta according to pkg directions; drain. Place half of pasta in an ungreased 13x9 baking dish. Top with half of meat sauce, sour cream, and Provolone cheese. Repeat layers. Sprinkle with Mozzarella cheese. Cover and bake 35-40 minutes. Uncover; bake 10 minutes longer or until the cheese begins to brown. Let stand for 10 minutes before cutting.