Toss eggplant with 2 teaspoon salt in a colander. Drain 30 minutes. Rinse, then squeeze out excess liquid and pat dry.
Preheat oven to 350°F with rack in middle.
Heat oil in a large heavy skillet over medium-high heat until it shimmers. Fry eggplant in 3 batches, stirring occasionally, until browned, about 5 minutes per batch. Transfer with a slotted spoon to paper towels to drain.
Discard all but 2 tablespoons oil from skillet, then sauté onion with 1/4 teaspoon each of salt and pepper until golden, about 8 minutes. Stir in sauce and eggplant and simmer 5 minutes.
Meanwhile, cook rigatoni in a pasta pot of boiling salted water (2 tablespoons salt for 6 quart water) until al dente, then drain. Stir together pasta, sauce, and half of mozzarella in pot. Transfer to a 3-quart baking dish and sprinkle with remaining mozzarella. Bake until cheese is melted and golden in spots, about 45 minutes. Let stand 5 minutes before serving.
