Athletic Bilbao, Malaga and Elche also won to complete the last 16.
Striker Mario Mandzukic slotted in Atletico's opener in the 19th minute and headed in a second in the 74th, seven minutes after Hospitalet's Ruben Alcaraz got his first goal. Mandzukic has 14 goals since arriving to replace Diego Costa for the Spanish champions.
Alcaraz struck again in the 84th with a long shot that sailed over goalie Jan Oblak and hit the crossbar before going in.
Oblak, however, spared Atletico an embarrassing loss with a one-handed save in the 89th.
Atletico will face cup holder Madrid in January.
Elche will meet Barcelona after it eked out a 1-0 win over second-tier Valladolid from Adrian Lopez's goal following their 0-0 first-leg draw.
Malaga, meanwhile, got a brace from striker Roque Santa Cruz to dispense with Deportivo La Coruna 4-1, moving on 5-1 overall.
Santa Cruz pounced on a defensive error to get his first in the 52nd. Helder Postiga briefly pulled Deportivo level in the 58th, only for Jose "Recio" Garcia del Pozo to score in the 60th before Santa Cruz and Ignacio Camacho turned it into a rout.
Bilbao took the lead from Borja Viguera's 38th-minute goal, and held on to oust Alcoyano 1-0, going through 2-1 on aggregate.
The elimination of Alcoyano, Hospitalet and Valladolid meant none of the 12 lower-division teams survived the round of 32, the first with the 20 teams from the top flight.
Hospitalet coach Kiko Ramirez echoed the sentiment of many in Spain who argue that the competition would be more exciting by a return to the single-game format to give smaller clubs a better chance at upsetting the bigger ones.
"The two-leg format hurts the more humble clubs because we can't compete," Ramirez said. "I would have deployed all my weapons (for one match). Playing one game would be better."