A new and distinct cultivar of Chrysanthemum plant named ‘Fichryevenpur’, characterized by its upright to outwardly spreading and uniformly and broadly mounded plant habit; moderately vigorous to vigorous growth habit; freely branching habit; dense and full plant form;;uniform and freely flowering habit; medium-size decorative-type inflorescences with deep purple-colored ray florets; mid to late season flowering habit, grown under natural season conditions, plants begin flowering in late September to early October in the United Kingdom; and good garden performance.