Prepare and bake the cake in a 13x9 pan according to the package instructions. Let cool completely before poking holes across the cake with the bottom of a wooden spoon. Be sure to poke all the way to the bottom of the pan.
16.25 ounce yellow cake mix
In a large bowl, whisk together pudding, milk, and vanilla, but don't let it thicken. Pour the thin pudding over cake in an even layer, poking down into the holes if necessary.