Benzema headed Madrid in front from Marco Asensio's cross just after half-time and nodded in a second when Athletic goalkeeper Iago Herrerin missed Luka Modric's corner. He saved the best until last as he chipped into an empty net after another Herrerin error in added time.
The former Lyon forward has now scored each of Madrid's last eight goals, taking him to 30 in all competitions for 2018-19.
"For me Karim is best No. 9 in the world, although there are many good players, and others might choose someone else," Zidane said in a postmatch news conference. "What he has been doing here over 10 years, means everything.
"His goals are impressive and I am happy for him. He has confidence in himself, always aims to improve. But his team were helping him, with Marco's cross, [Jesus] Vallejo's recovery of the ball to start off the move for the first goal."
Asked if this was the best performance since his return as Blancos' coach last month, Zidane said he was particularly impressed with his team's attitude and battling qualities.
"We played very well, even in the first half," he said. "We also started well, with rhythm, and just lacked a goal in the first half.
"I'm happy with the attitude as we played very well today. We kept a clean sheet, just giving up one chance with the cross to Inaki Williams. With second balls, set-pieces, aerial challenges, we were very focused today. Then we showed the quality we have."
Gareth Bale was again whistled during a substitute appearance. The former Tottenham man won the corner which led to Benzema's second goal and laid the ball off for the 31-year-old's third.
"The pity is that [Bale] had a chance to score, and I am sorry for him," Zidane said. "I would have liked to see Gareth score.
"As always I will not get involved [in talking about future]."
Asked if he understood why Bale was the subject of boos from the home fans, while other out of form players were not, he replied: "No, I don't understand that."
Meanwhile, defender Marcelo said rumours about him leaving the club were false and insisted that he was happy at Madrid.
The Brazilian, a key player at Real since arriving in 2007, lost his place to youngster Sergio Reguilon earlier this season and Spanish media reports have frequently linked him with a move to Juventus over the past six months.
"I'm focused on the club. Everything that's happened this season hasn't affected me at all," he said. "I carried on working hard, helping my teammates, whether playing or not.
"I've always been there with them, backing everyone. Whether you play or not is just part of the season and of being a footballer, but I have never stopped working or helping my teammates. If I play, then all the better.
"Everyone here knows how happy I am and I show it every day, either training or playing, wearing this shirt.
"A lot is being said about me on the outside. I think -- no I don't think, I know -- that Madrid is my home and those who know me know the truth."
Information from Reuters was used in this report