In a medium saucepan, combine sugars with orange peel and juice; bring to a boil over medium heat and boil 2 minutes. Reduce heat to medium-low, add cranberries and salt and cook, stirring until cranberries burst and sauce thickens, 8 to 10 minutes.
Remove from heat, add vanilla and butter and stir until butter is melted. Let sauce cool slightly, 10 to 15 minutes. Place pie crust on a rimmed baking sheet.
Pour filling into crust to within 1/4 inch of top rim. Bake 30 minutes. Place on wire rack and let cool 30 minutes.