The team from the town of Xativa near Valencia, known as the birthplace of Pope Alexander VI, held Real to a 0-0 draw on their artificial pitch in the first leg on Dec. 7, triggering celebrations by home fans in their 3600-capacity Campo de la Murta stadium.
Real, the world's richest club by income, whose annual revenue of more than 500 million euros ($687 million) dwarfs Olimpic's of around 600,000 euros, were dumped out of the Cup by Union at the last 32 stage in 2008 before suffering a similar fate against Alcorcon a year later.
He is likely to deploy at least some of his big guns on Wednesday to ensure they avoid another embarrassing slip-up.
"Madrid is a team from another galaxy," Olimpic coach Toni Aparicio, whose team competes in a league one level below Real's B team, said after the first leg.
"The team put on a good show and we worked extremely hard, what more can you ask?
"The pitch made it harder for them and the size does not help but the return leg will be easier for them."
Critics say the King's Cup format robs it of some of the drama seen in domestic knockout competitions in other countries as top-flight heavyweights here play their second legs against lower-league opponents at home.
That makes giant-killing much harder but if Olimpic somehow manage to pull off what would be one of the biggest shocks in Spanish Cup history, they will face either Malaga or Osasuna in the next round.
Malaga coach Bernd Schuster was in charge at Real when they were eliminated by Union five years ago and his current side surrendered a three-goal advantage at home to Osasuna in their first leg to draw 3-3, with the return to be played in Pamplona on Tuesday.
La Liga leaders Barcelona and Cup holders Atletico, 2-1 winners against Real in last season's final, both recorded comfortable wins at third-tier opponents in their first legs.
Barca came from a goal down to win 4-1 at Cartagena on the south coast and Atletico thumped Barcelona-based Sant Andreu 4-0 and the return legs are on Tuesday and Wednesday respectively.
Barca look to have an easier path to the final, with Real and Atletico on the other side of the draw and on course to meet in the last four.
($1 = 0.7283 euros)