Graphania averilla was first described by George Hudson in 1921 under the name Melanchra averill. The moth was discovered by Averil Lysaght in December 1920 on Mount Egmont. Alfred Philpott also described this species in 1924 under the name Melanchra furtiva from specimens collected around Mount Arthur as well as in the mountainous areas near Lake Wakatipu. In 1988 John S. Dugdale placed this species within the genus Graphania and recognised Melanchra furtiva as a new synonym.