Heat oven to 450°F. Make pie crust as directed on box for One-Crust Baked Shell using 9-inch glass pie plate. Cool completely, about 30 minutes.
Meanwhile, in large mixing bowl, mix pudding mix and coffee granules. Add 1 1/4 cups of the milk and the nondairy creamer; beat with wire whisk 2 minutes. Refrigerate.
In medium bowl, beat 1 cup of the whipped topping and 1/4 cup of the mocha cappuccino spread with wire whisk until blended. Refrigerate.
Spread remaining 1/2 cup mocha cappuccino spread in bottom of cooled pie crust. Carefully layer and spread the pudding mixture, the mocha whipped topping mixture and the remaining 1 cup whipped topping in pie.
In small microwavable bowl, mix remaining 1 tablespoon mocha cappuccino spread and remaining 1 teaspoon milk. Microwave on high 15 to 20 seconds or until melted; stir. Drizzle over pie. Refrigerate 1 hour before serving. Store covered in refrigerator.