Barcelona will face Valencia in the Copa del Rey semifinals while Real Madrid's conquerors Leganes take on Sevilla.
Barca have won the competition for the last three years and Marcelino's Valencia, who drew 1-1 with them in La Liga earlier, stand between them and another final.
The first leg takes place at the Camp Nou and Barca captain Andres Iniesta told the club's official website: "We want to play a great game at home to make the difference, we know Valencia will ask a lot of us.
"Any detail can settle the tie. We want to be back in the final -- we have won the last three and we want to win again."
Barca secured their place with a derby win over Espanyol, which featured a debut for former Liverpool playmaker Philippe Coutinho.
The draw means Valencia, who saw off Alaves on penalties, will face Real Madrid, Barca, Atletico Madrid and Barca again in an 11 or 12-day period.
In the other tie, Leganes will look to build on their memorable win over Real, but coach Asier Garitano will not allow his team to get carried away.
"I don't think it's our biggest achievement," he said on Thursday. "Going from the Segunda B [third tier] to the Segunda was more important.
"Now we are thinking about playing Espanyol in the league, then we'll think about the cup."
Sevilla beat Atletico Madrid 3-1 in Tuesday's second leg and 5-2 on aggregate to reach the last four.
Coach Oscar Arias said of his opponents: "Leganes are a more humble club but, given the stature of each team, they have done more to deserve being here than the rest of us and we have to respect that."
The first legs will take place on Jan. 31 and Feb. 1, with return fixtures a week later.