In the third tier in Spain, Toni Aparicio's men surprisingly held Real to a 0-0 draw in the first leg of the last-32 tie at the Estadio La Murta.
Carlo Ancelotti had the likes of Angel Di Maria and Isco in his starting line-up for the clash but they failed to find a goal away from home and need to increase their intensity after a lacklustre week, which has included draws versus Olimpic and Osasuna.
A trip to the Santiago Bernabeu shapes as a daunting test for Olimpic, even if Real are again without superstars Cristiano Ronaldo and Gareth Bale.
The visitors will need plenty of luck and it would be a huge shock if Ancelotti's men, third in La Liga after a 2-2 draw against Osasuna on Saturday, failed to progress.
Elsewhere, Barcelona host Cartagena carrying a 4-1 lead from the first leg after surprisingly falling behind to the Segunda B side.
Gerardo Martino is likely to rest several of his regulars with such a big advantage heading to the Camp Nou.
Reigning champions Atletico Madrid should do the same as they prepare to welcome Sant Andreu after winning the opening leg 4-0.
Several other top-flight teams have work to do if they are to advance to the last 16.
Relegation-threatened La Liga side Real Betis lead Segunda B outfit Lleida Esportiu 2-1 ahead of a home clash.
Real Sociedad only claimed a 1-1 first-leg draw versus Algeciras, while Getafe host Girona after their match finished with the same scoreline.
Levante trail second-tier Recreativo Huelva 1-0, Valencia were held 0-0 by another Segunda B team in Gimnastic Tarragona and Espanyol host Real Jaen after their 2-2 draw.
An all-La Liga tie between Elche and Villarreal is locked at 2-2 ahead of a meeting at the Estadio Manuel Martinez Valero, while Real Vallecano and Real Valladolid drew their opener 0-0.
Sevilla lead Racing Santander 1-0 and Athletic Bilbao must overturn a 1-0 deficit when they host Celta de Vigo.
Granada welcome Alcorcon with a 2-0 advantage, Almeria host Las Palmas leading 3-1 and Osasuna and Malaga meet after a thrilling 3-3 draw first-up.
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