Moments after Atletico threatened to go 2-0 ahead, Benzema drove the ball past Jan Oblak to earn a 1-1 draw that keeps Madrid clinging to hopes of a successful title defense.
They are not as close as they would hope; five points off the pace having played one more game than Atletico means there is a mountain to climb.
But that gap was almost eight points after Luis Suarez's early strike looked set to decide the derby, with Benzema's 88th-minute intervention a welcome reprieve for the visitors to the Wanda Metropolitano.
"It is deserved, we had chances at the end. We could have scored more, but the good thing was we had a different second half and changed the game," Zidane told a post-game news conference.
"It is a point, we are alive. We are going to keep fighting. It is a correct result, we believed until the end that it could be recovered."
Madrid thought they should have had a penalty late in the first half when a corner from Toni Kroos zipped across the six-yard box and struck Felipe on the arm, but referee Alejandro Hernandez Hernandez rejected the claims, even after viewing the incident on a touchline screen.
Perhaps Zidane might have had a different view if Benzema had not equalized, but Madrid's head coach offered a phlegmatic post-game perspective.
"His job is difficult. It is his decision, his responsibility. We have to respect that," Zidane said of the referee. "The players said it was a hand, he has reviewed it and decided not to whistle."
Atletico are three points ahead of second-placed Barcelona but finished this game deflated, and their once-commanding lead has been whittled away in recent weeks.
"We know there is a lot left," Zidane said. "Everything can always change, we are doing things well, we can improve.
"I am very proud of all my players. We are in the same boat and we are going to fight to the end."
Atletico have now gone 10 LaLiga derbies against Madrid without a win, drawing six of those games and losing four times.
The result also means Real Madrid have not lost any of their four LaLiga games at Atletico's new home (W1 D3), and they remain the only team to have played in the stadium in the Spanish top-flight without losing.
Zidane also avoided a rare defeat to Diego Simeone, meaning the Atletico boss now has just one victory in nine matches (W1 D5 L3) against the Frenchman in LaLiga. That 11 percent win record for Simeone is the Argentinian's worst against any manager he has faced at least four times in the competition.
Ultimately, Real Madrid set out to bring home all three points, yet the one they left with felt almost like a win.
Speaking to broadcaster Movistar, Zidane explained he was impressed by how greatly Madrid improved in the second half, after a shaky start to the game.
"We had to be more aggressive, be higher, have more pressure. We had to be more alive on the pitch," he said. "You can get into a bad game, but then you have to change.
"That's what we did in the second half, change at a general level, defensively and offensively.
"They are a direct rival. We wanted all three points. The important thing is to turn the game around. Now we have to continue."