L'Hospitalet 0 Atletico Madrid 3: Late goals put Atletico in charge
Antoine Griezmann ghosted into the penalty area 20 minutes after coming on at half-time to head Diego Simeone's side in front from close range in the first leg of the round of 32 clash.
Alessio Cerci and Raul Jimenez had come close in the first half, but it was the introduction of France international Griezmann that gave the visitors the cutting edge they had lacked.
Raul Jimenez almost doubled their lead with 15 minutes to play, before the La Liga champions were able to double their lead courtesy of Gabi's penalty after Cerci had been upended.
Cristian Rodriguez then added a third goal in stoppage time and Atleti will be expected to secure their place in the fifth round when the two sides meet in the second leg at the Vicente Calderon on December 18.
Simeone gave a first-team debut to 18-year-old Lucas Hernandez, while Jan Oblak and Cerci were handed their first domestic starts for the 2013 winners. The hosts were without top scorer David Haro, who dropped to the bench.
After a slow start the visitors began to find their rhythm on the artificial surface, and were unlucky not to take the lead after 11 minutes.
Rodriguez delivered a dangerous cross from the left towards Cerci, who met the ball first time but Oliver Sanchez got down well to push the ball away.
Oliver was beaten eight minutes later, but the crossbar came to his rescue when Jimenez's header clipped the woodwork after he was picked out by Cerci.
L'Hospitalet showed brief glimpses that they could pose a threat going forward, but Atletico continued to look more likely to open the scoring and were frustrated again when Saul and Cerci wasted good chances in the closing minutes of the first half.
No doubt with Simeone's words ringing in their ears Atletico were much more attacking in the early stages of the second half, with substitute Griezmann making an immediate impact.
Griezmann saw an attempted cross hit the bar within two minutes of the restart, and then set up Jose Gimenez, but his effort was cleared off the line.
Atletico did have the ball in the net on 49 minutes as Gimenez reacted quickest after Oliver had failed to collect a corner, however the assistant referee denied him the opening goal as he flagged for offside.
It was no surprise when Griezmann got the game's opening goal 66 minutes in, the forward escaping the attentions of his marker to meet a Jesus Gamez cross with a deft header past Oliver.
After Jimenez had fired a low shot wide Atletico were handed a second goal when Cerci was pulled down in the penalty area by Agustin Fernandez
Gabi assumed responsibility from the spot, and he made no mistake and there was still time for a third goal for the visitors.
It was Rodriguez who gave the scoreline a more emphatic look with a stunning left-footed strike in stoppage time, the ball swerving out of Oliver's reach from 25 yards.