France international Mendy blasted in the opener after 10 minutes.
The 25-year-old defender accelerated down the left wing between Victor Diaz and Dimitri Foulquier before firing into the roof of the net from an acute angle for his first goal for Madrid since moving from the French club Lyon in June 2019.
When Mendy's compatriot Benzema added the second six minutes later, Real seemed in cruise control at the Estadio Nuevo Los Carmenes.
But five minutes after the pause, Darwin Machis halved the deficit.
Struggle
An increasingly nervous Madrid were clinging on in the closing stages and needed skipper Sergio Ramos to clear one shot off the line before securing a ninth consecutive victory since Spanish football resumed after the government lockdown to stem the spread of the coronavirus pandemic.
"Our vision when we start every season is to win the league," said Zidane. "There are two games left. We are close but we're not there yet."
Madrid could claim La Liga for the first time since 2017 at the Alfredo di Stefano Stadium on Thursday night. "It would mean a lot," said Ramos.
"We can't relax. We're a bit closer but we have to carry on. We let our guard down a bit in the second-half against Granada and maybe that's a warning for us. We have to make sure we don't repeat that mistake."
Ramos, a winner of four La Liga titles in his 15 years at Madrid, added: “The league is the prize for consistency over the whole year.
"Maybe we had a period of reflection during the suspension and we came back and reacted. We're in the race and hopefully on Thursday we can celebrate."
.
