Heat oven to 350 degrees F. Grease an 8-inch square baking pan.
Mix first 5 dry ingredients in the prepared baking pan. Make 3 depressions in dry ingredients – two small, one larger. Pour vinegar in one small depression, vanilla extract in the other small depression and the vegetable oil in third larger depression. Pour water over all. Mix well until smooth.
Bake on middle rack of oven for 35 minutes. Check with a wooden pick to make sure it comes out clean. Cool.