Atletico Madrid were far from their best but progressed to the Copa del Rey quarter-finals after Marcos Llorente scored one and assisted another in a 2-0 victory at Levante.
Diego Simeone's side have won just one of their last six LaLiga games and their recent struggles were evident despite victory over second-tier Levante on Wednesday.
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 await the identity of their next opponents in Friday'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.
What does it mean? Atleti's silverware hopes rely on Copa del Rey
Out of Europe after finishing bottom of Champions League Group B and 13 points adrift of LaLiga leaders Barcelona, Atletico's quest for silverware relies solely on the Copa del Rey.
Simeone's side are yet to face a top-flight side in this competition, although they have battled past Almazan, Arenteiro, Real Oviedo and Levante with relative ease.
However, with Real Madrid and Barcelona – who face Ceuta and Villarreal respectively on Thursday – still in the competition, Atletico will have to improve to lift their first Copa del Rey in 10 years.
De Paul controls the game
Atletico were not especially impressive but maintained control with the help of Rodrigo De Paul.
The Argentina midfielder, appearing in his first game since lifting the World Cup in Qatar, enjoyed the most touches (97) and most successful passes (70) of any player while winning all of his five duels.
Livewire Bouldini blunted
Bouldini was a constant livewire up top as he acted as a nuisance for Atletico's centre-back partnership of Mario Hermoso and Stefan Savic.
The Levante forward attempted four shots and contested a remarkable 21 duels – both marks the most of any player – though his hard-working ethic did not make up for his or Levante's lack of quality in front of goal.
Atletico return to LaLiga action at home to Real Valladolid on Saturday.