Diego Simeone's side has won just one of its last six LaLiga games and its recent struggles were evident despite victory over second-tier Levante on Thursday (AEDT).
Atletico's first shot on target in the 54th minute through Morata opened the scoring after Llorente's cross before the midfielder sealed progression with a calm stoppage-time finish.
The LaLiga side awaits the identity of its next opponent in Saturday's last-eight draw as they aim for a first Copa del Rey crown since 2013.
Alex Munoz finished into an empty net when Jan Oblak fumbled after 25 minutes, yet the goalkeeper's blushes were spared as a free-kick was awarded for Mohamed Bouldini's heavy aerial challenge.
Bouldini arrowed a fizzing left-footed effort narrowly over soon after as an underwhelming Atletico failed to impose themselves on a first half devoid of quality.
However, a touch of class after the restart brought the opener as Antoine Griezmann danced through the middle before finding Marcos Llorente, who rolled across for Morata to finish into the bottom-left corner.
Oblak intervened at a crucial moment when Bouldini appeared positioned to net an equaliser, before a sweeping counter-attack at the other end ensured victory for Atletico.
Griezmann orchestrated the break from inside his own half before Nahuel Molina played in Llorente, who slotted a right-footed finish past Joan Femenias.
