It also helps dry up oily areas and works like a natural antibiotic to heal blemishes.Foods rich in vitamin A include carrots, watercress, sweet potatoes, leafy greens, milk and egg yolk.Vitamin A is fat-soluble so your body will absorb it much better if you pair it with some healthy fats such as olive oil or avocado.Zinc is a mineral that helps reduce oil production in the skin.