Ronaldo was slapped with a five-game ban for pushing the referee after he was sent off in the first leg, but his replacement Marco Asensio enhanced his reputation as one of world football's rising stars as he smashed Madrid into the lead after just four minutes.
Karim Benzema then deservedly doubled Real's lead before half-time.
Barca responded with a more spirited second-half showing and were unfortunate not to at least pull a goal back as Lionel Messi and Luis Suarez hit the woodwork.
"We played a great match tonight," said Zidane. "Especially in the first half it was spectacular."
Zidane even had the luxury of leaving first-team regulars Gareth Bale, Isco and Casemiro on the bench as Real's strength in depth was demonstrated in a dominant first 45 minutes.
"This team has hunger and every time we play it shows," added Zidane.
"We have to try to continue like this. To start the season like this is very good, but we know a long season is just starting."
"I think we were superior across the whole tie," Asensio told Spanish TV station Telecinco.
However, he rejected suggestions he is now ahead of Bale in Zidane's pecking order.
"I am working to have as many minutes as possible on the field.
"I am happy on both a collective and individual level."
- Barca 'on the ropes' -
========================
Barcelona boss Ernesto Valverde has suffered the worst possible start to his reign with back-to-back defeats against the Catalans fiercest rivals and the visitors never threatened to mount a comeback after conceding.
Shorn of Neymar after his world record breaking transfer to Paris Saint-Germain and injured captain Andres Iniesta, Barca's star front two lacked the service needed to make a meaningful impact.
"In three days we find ourselves against the ropes," added Valverde.
"Things have happened in pre-season that have affected the balance of the team and our job is to refind that balance."
Indeed, the scoreline could have been a lot more embarrassing for Barca as Marcelo dragged wide before Lucas Vazquez hit the post with a glorious chance.
An 11:00 pm kick-off time meant half-time saw Wednesday turn to Thursday and Barca did at least salvage some pride in the early morning with an improved second-half display.
Messi was desperately unlucky not to net a consolation goal as he hit the underside of the bar from a narrow angle.
The visitors' night was summed up when Suarez headed against the post with the goal gaping after Navas had parried Messi's driven shot into his path.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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