Enzo, the oldest of Zidane's four sons, was introduced by his father, a legendary former player for Real and France, at half-time.
Madrid: Real Madrid coach Zinedine Zidane's son, Enzo, scored on his senior debut as the European champions brushed aside third tier Cultural Leonesa 6-1 to progress into the last 16 of the Copa del Rey 13-2 on aggregate on Wednesday.
Enzo, the oldest of Zidane's four sons, all of whom play at different levels in Real's youth teams, was introduced by his father, a legendary former player for Real and France, at half-time.
The 21-year-old, who was previously coached by Zinedine at Real's youth side Castilla before he took the top job at the Santiago Bernabeu in January, showed a glimpse of his father's talent with a fine low finish from the edge of the area just after the hour mark.
"If I take off my hat as a coach then I am happy for him as a father (too)," said Zidane.
"But, in saying that, I watch what he does on the field as a coach and I am happy with how they all played."
With the tie over as a contest following Real's 7-1 first leg win and El Clasico away to Barcelona to come on Saturday, Zidane made nine changes from the side that started the 2-1 win over Sporting Gijon last weekend.
Norwegian starlet Martin Odegaard, 17, was also handed his full debut, but it was Dominican international Mariano Diaz who got Real off to a flying start as he slotted home the first of his hat-trick after just 23 seconds.
James Rodriguez headed home the hosts' second before Mariano smashed in a third, but Leonesa did have a moment to savour when Yeray Gonzalez fired into the top corner from long range in first-half stoppage time.
Enzo was then handed his long-awaited bow by his father, but ensured there was to be no claims of nepotism when he finished off a flowing team move with a classy right-footed finish.
Mariano completed his hat-trick two minutes from time before a Cesar Morgado own goal.
Yannick Carrasco scored twice as Atletico Madrid also hit Guijelo for six in the first leg of their last 32 tie.
A Saul Niguez penalty and Sime Vrsaljko's first Atletico goal gave the visitors a 2-0 half-time lead before the Belgian struck twice in five second-half minutes.
Angel Correa and Roberto Nunez rounded off the scoring.
Sevilla and Villarreal also took huge strides towards the last 16 with comprehensive first leg wins.
Joaquin Correa scored a hat-trick in Sevilla's 5-1 win at Formentera, whilst Villarreal cruised to a 3-0 victory at Toledo.
Second division Cordoba produced the only upset of the evening with a 2-0 win over Malaga.
Holders Barcelona begin their defence later on Wednesday at Hercules.