Zidane introduced his eldest son at the break and it took him just 18 minutes to find the net.
The 21-year-old midfielder was brought on by his father, the Madrid coach, at half-time in their Copa del Rey victory over Cultural Leonesa at the Bernabeu.
Real led 7-1 from the first-leg and raced into a three-goal lead before the Spanish minnows pulled one back.
Young striker Mariano Diaz scored a hat-trick for Real as they eased into the next round.
Madrid won the tie 6-1, beating their third-tier opponents 13-2 on aggregate to reach the competition's last 16.
Norwegian teenager Martin Odegaard, who signed as a 16-year-old in January 2015, also made his full debut.
Enzo, the eldest of Zidane's four sons, made almost 50 appearances for Madrid's reserve team before being given his senior debut.
Enzo Zidane scored on his Real Madrid debut in their clash with Cultural Leonesa.