Preheat oven to 425 degrees F (220 degrees C). Grease 2 baking sheets.
Beat sugar, margarine, orange zest, vanilla extract, salt, and baking powder together in a large bowl until blended. Stir in flour, applesauce, and cranberries until dough is well combined.
Drop dough onto baking sheets by tablespoons, 2 inches apart; flatten slightly.
Bake in the preheated oven until edges are golden brown, 6 to 7 minutes. Let cool for 5 minutes; transfer to a wire rack to cool completely, about 15 minutes.