Spread potatoes, zucchini, and red onions in a 9x13-inch baking dish, or preferably a larger one. Use 2 baking dishes if necessary. Cover with pureed tomatoes, olive oil, parsley. Season with salt and freshly ground pepper. Toss all ingredients together so that the vegetables are evenly coated.
Bake in the preheated oven, stirring after 1 hour, until vegetables are tender and moisture has evaporated, about 90 minutes. Cool slightly before serving, or serve at room temperature.