Despite their opponents losing Raul Garcia to a 12-minute red card, the Spanish champions needed to battle for all three points on Tuesday evening.
Toni Kroos' opener on the stroke of half-time was quickly cancelled out as Ander Capa equalised for Athletic shortly before the restart.
But, as has so often been the case down the years, Benzema came to Real's rescue with a late double to secure an important La Liga victory.
That contribution led Zidane proclaiming his compatriot as the best centre-forward France has ever produced - ahead of the likes of Thierry Henry, Michel Platini and Just Fontaine.
"For me, yes," the coach said when asked about the possibility of Benzema surpassing his countrymen. "He shows it with what he's doing. He's played at Real Madrid for a long time, more than 500 games.
"His goals, his trophies, what he's done, they speak for themselves. For me he's the best, yes, it's clear.
"He's the best. Without playing a really good game today, he scored twice again. He always shows up, that's what the great players do."
Zidane went on to highlight Benzema's unselfishness as perhaps his favourite thing about the forward's game.
"He isn't a pure No. 9, only thinking about goals," he added.
"That's why I love him. He doesn't only have that in his head. He links up, passes to teammates. That's what I like in football, and he has both things."