Heat the oven to 400°F.
Cook the beef and garlic in a 12-inch skillet over medium-high heat until the beef is well browned, stirring often to break up the meat. Pour off any fat. Add the zucchini and cook until it's tender. Stir in the sauce.
Stir the beef mixture, pasta, 1/2 cup mozzarella cheese, ricotta cheese and Parmesan cheese in a 3-quart shallow baking dish. Sprinkle with the remaining mozzarella cheese.
Bake for 20 minutes or until the mixture is hot and bubbling and the cheese is melted.