A new and distinct Petunia cultivar named ‘DAMORFIEST’ is disclosed, characterized by a mounded growth habit and flowers uniquely colored burgundy with yellow stripes. The plants are very well branched with a medium vigor. Light intensity and weather conditions can influence the width of the stripes, creating shapes resembling hearts. The flowers are large and plants flower abundantly. The new variety is a Petunia, normally produced as an outdoor garden or container plant.