Real Madrid must again overcome lower-league opposition in the Copa del Rey last 16, while Barcelona have been handed a tricky tie at home to Leganes.
Zinedine Zidane's Madrid survived a scare against Unionistas de Salamanca in the previous round, securing a 3-1 win away from home, with Gareth Bale and Brahim Diaz getting on the scoresheet.
The Blancos have been rewarded with a visit to Real Zaragoza, who are currently fourth in the Spanish Segunda as they bid to return to the top flight.
Barcelona were also tested by minnows in the round of 32, scraping past Ibiza, thanks to a brace from Antoine Griezmann.
They now have the benefit of a home fixture as they bid to reach the quarter-finals of this year's competition.
With La Liga sides kept apart where possible, the Blaugrana were selected in one of just two ties solely involving top-tier teams.
They will face Leganes at Camp Nou while the majority of their top-flight rivals take in ties away from home.
Segunda B side Cultural Leonesa defeated Atletico Madrid 2-1 in extra-time on Thursday, which was undoubtedly the biggest shock of the entire round.
They will now move on to a huge clash with Valencia, who beat Barca in last season's final to lift the trophy - ending their rivals hopes of a domestic double in the process.
Badajoz, the only other third-tier side remaining in the competition, also have La Liga opposition to contend with in the form of Granada.
The second all-La Liga tie saw Real Sociedad drawn at home to Osasuna.
Copa del Rey last-16 draw in full
Badajoz v Granada
Cultural Leonesa v Valencia
Tenerife v Athletic Bilbao
Real Zaragoza v Real Madrid
Mirandes v Sevilla
Rayo Vallecano v Villarreal
Barcelona v Leganes
Real Sociedad v Osasuna