Diego Simeone's men produced an unremarkable second-leg display in front of a sparse crowd at the Vicente Calderon, with Ruben Alcaraz twice pegging Atletico back to cancel out Mario Mandzukic's brace.
Atletico were also fairly unconvincing in their 3-0 first-leg victory at the Segunda B3 side, although Kiko Ramirez's team were far more clinical in the return game.
Mandzukic opened the scoring in the 19th minute, stroking beyond goalkeeper Carlos Craviotto after a kind ricochet, but the hosts failed to make the most of their other chances.
Alcaraz pulled the visitors level in the 64th minute with a deflected effort before Mandzukic had seemingly given Atletico a 2-1 win with 16 minutes to go.
But Alcaraz netted again in the final 10 minutes, beating Jan Oblak with a spectacular long-range effort to secure an unlikely 2-2 draw, with Atletico going through 5-2 on aggregate to face holders and bitter rivals Real Madrid in the last 16.
Simeone resisted the urge to make wholesale changes to his team following the weekend defeat to Villarreal, but defenders Lucas Hernandez and Ivan Perez made the leap up from the reserves, with the latter making his first-team debut.
Following a low-key start, Atletico eventually broke the deadlock when Mandzukic steered home after pouncing on Mario Suarez's blocked effort.
Craviotto made a crucial save of his own to deny Atletico a second on the stroke of half-time, keeping out Mandzukic's volley from point-blank range after a clever header from Jesus Gamez.
Atletico seemingly began the second period with a little more urgency and Craviotto was tested again within two minutes of the restart, diving down to his left to keep out Raul Jimenez's low drive.
The hosts went close again in the 65th minute, but Saul knocked the ball right across the face of goal after getting on the end of Koke's fine free-kick delivery.
Mandzukic swiftly restored Atletico's lead with a diving header from Koke's cross at the back post, but L'Hospitalet continued to battle away.
