A new and distinct cultivar of Chrysanthemum plant named ‘G22MAG13BR’, characterized by its upright, outwardly spreading and uniformly rounded plant habit; moderately vigorous growth habit; freely branching habit; dense and full plant habit; flexible stems; dark green-colored leaves; uniform and freely flowering habit; long flowering period; medium-sized decorative type inflorescences with ray florets that are reddish bronze in color; and excellent garden performance.