Preheat oven to 350ºF. Grease one 9x5 loaf pan and set aside.
Sift together flour, baking soda, baking powder, salt and cinnamon into a bowl and set aside.
In a separate bowl stir together eggs, oil, applesauce, sugar, zucchini and vanilla. Make sure it is fully combined and the ingredients are no longer separated.
Carefully pour flour mixture into egg mixture, stirring until just combined and no more flour is visible.
Pour entire mixture into loaf pan. Bake 50-55 minutes, or until middle is set.