Atletico boss Diego Simeone played a near full-strength team in an effort to avoid another disappointing showing in a difficult season.
His side, who finished last in their Champions League group and are fourth in LaLiga, having won only one of their last six games, went into the break having had no shots on target.
It took 54 minutes for Atletico to break the deadlock when substitute Angel Correa sprinted up-front and saw his teammate Marcos Llorente ghost into empty space in the right channel and delivered a ball through.
Llorente got into the area before putting it on a plate for Morata, who was waiting at the far post to tap into the empty net.
Llorente secured Atletico's spot in the quarter-finals in the 91st minute on a quick counter, receiving a long ball from full back Nahuel Molina in space and finishing with a precise shot to the goalkeeper's right.
Earlier on Wednesday, Valencia beat Sporting Gijon 4-0 and Athletic Bilbao beat Espanyol 1-0 also to advance to the quarter-finals. Real Sociedad and Sevilla were already through after wins on Tuesday.
Real Madrid will face Villarreal and Barcelona will travel to Ceuta to round off the last 16 on Thursday.
