Carlos Fernandez scored twice as Deportivo came from behind in the first leg to establish a dominant position in the tie.
Despite Malaga recording 25 shots in the return match, Jose Luis Marti's side held firm to secure a spot in the final.
Malaga had its chances, with winger Javi Ontiveros — the scorer of a delightful goal in Galicia — twice denied by the woodwork in a frantic first half, but goalkeeper Dani Gimenez remained unbeaten.
His opposite number Munir Mohamedi handed Depor victory in the second leg by allowing a speculative Alex Bergantinos drive slip out of his grasp in the 82nd minute, although a comeback already looked well beyond Malaga.
Depor will face either Real Mallorca or Albacete for a place in LaLiga next season, with the former holding a 2-0 lead from the first leg at Son Moix.