The task was made harder in first-half stoppage time when Diego Costa pounced on a mistake to fire Atletico into a 3-0 lead on aggregate.
The home side had chances in the second period and scored a late penalty through Jorge Molina, but Atletico advanced to book a semi-final meeting against Sevilla.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
BETIS: Casto; Perquis, Nacho, Lopez, Amaya; Sevilla, Benat, Perez, Vadillo; Castro, Campbell
ATLETICO: Courtois; Miranda, Luis, Godin, Manquillo; Gabi, Suarez, Koke, Turan; Adrian, Costa