Marco Asensio and Alvaro Morata each struck twice in a one-sided match, but Spanish international Morata should have had at least a hat-trick as Real ran riot, ensuring the return leg at the Santiago Bernabeu is effectively a dead rubber.
Madrid forward Mariano also got on the scoresheet but the best goal of the night came from defender Nacho, who fired in a wonderful acrobatic volley for Zindane's side.
Meanwhile, Benja scored a consolation goal for the third-tier minnows.
Real Madrid's forgotten man Fabio Coentrao made his return following seven months out injured on a routine evening for the Champions League winners.
Real, who have won the Copa del Rey 19 times, were thrown out of last season's competition after fielding the ineligible Denis Cheryshev in a tie with Cadiz.