Preheat oven to 350°F (175°C) and grease a 9x13-inch baking dish.
In a mixing bowl, combine yellow cake mix, eggs, and water. Mix until smooth and pour into the prepared dish. Bake for 25-30 minutes or until a toothpick comes out clean.
Cool for 10 minutes; poke holes in the cake with a fork.
In another bowl, whisk together instant vanilla pudding mix and milk until thickened (about 5 minutes). Slice bananas and set aside.
Pour half of the pudding mixture over the warm cake, allowing it to seep into the holes. Layer sliced bananas on top, then pour remaining pudding mixture over.
Spread whipped topping over the cake and chill in the refrigerator for at least 4 hours before serving.
