An epic fightback saw them through 5-4 on aggregate after they overturned a daunting 3-0 first-leg deficit.
Portugal winger Simao curled his effort into the top corner six minutes from time after they looked to have blown their earlier good work against the second division visitors.
Simao had set Atletico on their way after 22 minutes and further goals from Sergio Aguero and Tomas Ujfalusi had them 3-0 up at the break.
Aguero's shot was then deflected into the Recre net by visiting defender Troest after 62 minutes, but Atletico went on to press the self-destruct button.
Midfielder Paulo Assuncao was caught in possession in his own area allowing Carmona to grab an all-important away goal for Recre in the 71st, and then got himself sent off two minutes later for a second bookable offence.
But, despite being a man down, Atletico continued to press and Simao grabbed his second goal to set up a last-eight meeting next week with another second division side Celta Vigo.
"It was a spectacular game. We are starting to see the light at the end of the tunnel in the league as well but we must remain prudent," coach Quique Sanchez Flores told reporters.
"The player's are euphoric but the emotions must be for the fans, we have to focus on our next game. We shouldn't get carried away."
STOPPAGE-TIME GOAL
Earlier, a stoppage-time goal sent Real Mallorca into the quarter-finals after a 3-1 win over second division Rayo Vallecano put the La Liga side through 4-3 on aggregate.
Mallorca substitute Mario Suarez fired in from close range to complete an exciting comeback and avoid extra time at a rainswept Ono Estadi.
Visiting Rayo, who won the first leg 2-1 last week, had opened the scoring with a breakaway effort from striker Piti on the stroke of half-time.
Mallorca, who have won every home game this season, rallied with Victor heading the ball into the net at a corner in the 50th and then firing home at the far post 10 minutes later.
Mallorca will meet Getafe in the last eight.
The other two quarter-finals see Sevilla, who knocked out holders Barcelona, play Deportivo Coruna, and Racing Santander take on Osasuna.
