In a 5- to 6-quart pan over high heat, bring about 4 quarts water to a boil. Add penne and cook, stirring occasionally, until tender to bite, 10 to 12 minutes. Drain.
Pour oil into the same pan over medium-high heat. Add sausage and garlic and stir, breaking apart with spoon, until sausage is crumbled and brown, about 10 minutes.
Add chard and stir until wilted, about 5 minutes. Stir in tomatoes with juice, salt, pepper, and cooked pasta. Pour mixture into a 2- to 2 1/2-quart baking dish. Sprinkle mozzarella and parmesan cheeses over the top.
Bake in a 350° oven until cheese is browned and bubbling, 25 to 30 minutes.