Llorente stars as Atleti reaches quarter-finals
Diego Simeone and Atletico Madrid will have much to ponder despite beating Levante in the Copa del Rey last 16 on Wednesday.
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.