Diego Simeone's men held a two goal lead from the first-leg and progressed despite a double from Marko Livaja and a late Mateo Garcia strike
Despite losing 3-2 to Las Palmas on Tuesday, Atletico Madrid booked their place in the last-eight of the Copa del Rey having won 4-2 on aggregate.
Diego Simeone's men had a 2-0 lead from the first-leg, and were able to build on it when Antoine Griezmann opened the scoring for the home side just four minutes into the second-half.
Marko Livaja pulled one back for Las Palmas, but Angel Correa responded just a few minutes later with a goal to return Madrid to a comfortable position.