Real have not suffered a defeat to their neighbours since 1999, have a 100 percent home record this season and rattled eight goals past Levante at the Bernabeu in the previous round.
While Real's Jose Mourinho was in Zurich collecting FIFA's inaugural Coach of the Year award on Monday, Atletico were in Alicante suffering a humbling 4-1 La Liga reverse against promoted Hercules.
Last year's cup finalists, who had only conceded one goal in their previous four outings, were 4-0 down by halftime at the Rico Perez with the first two coming from defensive errors.
"It's inexplicable," said coach Quique Sanchez Flores. "This happens a lot with Atletico, I have never understood it.
"It's the same team that played three finals and won two trophies (Europa League and European Super Cup) in 2010. There is the need for a lot of psychological work with this team because it is one that never ceases to surprise."
That unpredictability and a change in competition may be their best hope for a turnaround in derby fortunes, though the priority will be keeping the tie alive for the second leg at the Calderon next week.
Villarreal, third in the league, lost 4-2 at Real on Sunday and now face holders Sevilla at the Madrigal on Wednesday.
Second division leaders Real Betis have to travel to play La Liga leaders Barcelona, who are unbeaten in 26 matches in all competitions, on Wednesday.
Betis were brutally realistic about their chances of progressing to the semis.
"Our daily battle, the thing that allows us to feed ourselves, is the league," defender Isidoro Gomez told reporters.
"This is a game to enjoy... not one to get carried away with for things that are not within our reach."
The other quarter-final sees Almeria host Deportivo La Coruna on Thursday.
