To cut clean slices, dip a sharp knife into water before each cut.
Heat the oven to 350 degrees. Grease or spray with cooking spray, and flour a 13x9-inch pan.
In a large bowl, combine the cake mix, 3 tablespoons flour, melted butter, and an egg. Mix until crumbly. Reserve 3/4 cup of the crumb mixture. Press the remaining mixture evenly into the pan.
In a large bowl, combine the cream cheese, powdered sugar and remaining flour. Beat on low speed until mixed and then beat on medium speed until creamy. Add the sour cream and remaining egg; beating on medium speed until creamy.
Spread the cream cheese mixture over the crust. Drop small spoonfuls of cranberry sauce over the top of the cream cheese layer.
Top the cranberry cream cheese layer with the reserved crumb mixture.
Bake for 38 to 42 minutes or until golden brown and the filling is set. Cool completely (about 1 hour). Refrigerate for at least 1/2 hour before cutting into bars.