However, Jorge Andrade equalised for Deportivo right on the stroke of half time and Pedro Munitis sealed the tie with a second for the visitors three minutes after the break.
Deportivo now go through to the final play French side Marseille.
Newcastle: Given, Carr, Elliott, Emre (Brittain 90), Boumsong, Shearer, Bowyer, Faye (Ameobi 53), Milner (N'Zogbia 72), Parker, Taylor. Subs Not Used: Harper, Ramage, Chopra.
Deportivo La Coruna: Molina, Manuel Pablo, Andrade, Capdevila, Romero, Duscher, Scaloni, Sergio (Valeron 72), Munitis, Ruben Castro (Juanma 63), Tristan (Luque 55). Subs Not Used: Dani Mallo, Victor, Acuna, De Guzman.