Bale scored a hat-trick and Benzema bagged a brace as Real surged to a comfortable 5-0 victory over Deportivo La Coruna at the Santiago Bernabeu.
There will surely be stiffer tests for Real in the weeks ahead, particularly defensively, but Zidane was content with the effort his players exhibited in what was a wholly dominant and attacking display.
"Whenever you win you have to be happy," Zidane told reporters after the match. "What I liked most was the attitude shown by the team. It is not easy to score five goals against a team like Deportivo la Coruna."
Real fans had been vociferous in their dislike of what they saw as the more defensive style offered up by previous boss Rafael Benitez, who was replaced by club-legend Zidane earlier this week
But hopes of excitement were high when it was confirmed Zidane would back up the potent attacking triumvirate of Bale, Benzema and Cristiano Ronaldo with a forward thinking midfield for his first fixture in charge.
Colombian playmaker James Rodriguez was the man to miss out with Toni Kroos, Luka Modric and Isco occupying the available midfield berths.
And although Real keeper, Keylor Navas, was forced to make an early save from Deportivo striker Lucas Perez, it was the home team that soon stamped its authority on the game.
Benzema flicked home from close range after 15 minutes to settle any lingering Real nerves.
Bale then made it two seven minutes later. The Welshman, who has had his critics at the Bernabeu since signing for a record $132 million in 2013
, nodded home Dani Carvajal's cross from six yards out with consummate ease.
Bale added a third shortly after the break when he sidefooted Ronaldo's cutback home from the edge of the 18-yard box.
And the hat-trick came on the hour mark as Bale soared above everyone to thump a header past German Lux in the Deportivo goal.
Real took its foot off the gas soon after and introduced substitutes James and Jesse.
But Ronaldo remained keen to get himself on the scoresheet, peppering Lux's goal with shots seemingly whenever he was within shooting range.
It looked like the Portuguese would finally score in injury time. But when he was tackled stretching for a Jesse cutback Benzema was on hand to ram home off the crossbar.
The result means Zidane's side now lie one point behind second-placed Atletico Madrid in the La Liga table and two behind leaders Barcelona.
Atletico can overtake Barca at the top of the table if it wins on the road against Celta Vigo Sunday.
The Catalans, however, will retain a game in hand at the end of the weekend's fixtures.