The invention provides seeds and plants of tomato hybrid SVTJ7513. The invention thus relates to the plants, seeds, plant parts, and tissue cultures of tomato hybrid SVTJ7513 and to methods for producing a tomato plant produced by crossing such plants with themselves or with another plant, such as a tomato plant of another genotype. The invention further relates to seeds and plants produced by such crossing. The invention further relates to plants, seeds, plant parts, and tissue cultures of tomato hybrid SVTJ7513 comprising introduced beneficial or desirable traits.