The hosts, runners-up in 1978, booked a spot in the last 32 courtesy of goals in either half from Guzman Casaseca Lozano and Asdrubal Padron.
Numancia, who sit 14 places below Las Palmas in the Segunda Division, saw Luis Valcarce dismissed on the stroke of half-time, dashing their hopes of a comeback.
But they will not have to wait long for a shot at revenge as the two teams meet in the league on Saturday.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.