Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan.
In a large mixing bowl, combine the yellow cake mix and instant lemon pudding mix.
Add the eggs, vegetable oil, water, and vanilla extract to the dry ingredients.
Using an electric mixer, beat the mixture on medium speed for 2 minutes until well blended.
Pour the batter evenly into the prepared baking pan.
Bake in the preheated oven for 28 to 32 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack before serving.