Benzema scored the only goal as Real Madrid edged past Granada. PHOTO: AFP
Atletico Madrid remain just a point behind their city rivals as Fernando Torres came off the bench to inspire Diego Simeone's men to a 2-0 win at Eibar.
Real had scored 15 times in their previous three matches, but they were grateful to some poor Granada finishing and controversial calls by the officials to claim all three points.
Benzema grabbed the only goal of the game nine minutes into the second-half with a cushioned header from Isco's fine cross.
Victory moves Madrid a point ahead of Barcelona at the top of the table with the Catalans not in action until Sunday when they host Levante.
"We knew before the game it could be a difficult game, against a good team that counter-attacks well, and that was how it was," said Madrid boss Rafael Benitez.
"We lost possession that allowed them to counter-attack and we didn't take our chances which complicated the game.
"I know we have to win and play well, but when the game doesn't go as you wish, to win and get the three points is very important."
The scene appeared to be set at a sunny Bernabeu for Cristiano Ronaldo to surpass Raul to become Madrid's all-time top goalscorer.
There was even a special introduction for the World Player of the Year as his mascot for the day was Zaid Mohsen, the seven-year-old Syrian refugee made famous when he and his father were tripped by a Hungarian camerawoman.
However, the script wasn't followed once the action got underway as Granada passed up a host of chances to spring a massive surprise.
Marcelo was forced into a clearance off the Real goal-line early on before Isaac Success fluffed his first of a number of opportunities when he failed to hit the target when unmarked at the back post.
Ronaldo's first opening came 18 minutes in, but Andres Fernandez stood up well to block his effort before Benzema failed to turn the rebound home.
Youssef El-Arabi did have the ball in the net for Granada moments later, but was wrongly ruled to have been offside.
Fernandez made further good saves from Luka Modric, Ronaldo and Lucas Vazquez to keep Benitez's men at bay.
Yet, Success had two more great chances to put Granada in front just before and after the break as he was denied by a brave save from Keylor Navas before chipping the ball well over with his second effort.
The Andalusians were eventually made to pay for their profligacy when Isco's perfect cross picked out Benzema for a simple header to open the scoring.
El-Arabi should still have given Granada a share of the points, but he too couldn't find a way past Navas at the end of a fine individual run as the Costa Rica international stretched his unbeaten streak to five games.
Atletico boss Diego Simeone made just one change from the side that won 2-0 at Galatasaray in the Champions League in midweek, but it wasn't until he introduced Torres after the break that the visitors took control against the Basque minnows.
Correa had only been on the pitch for a matter of seconds before Torres fed him to fire home his first goal for the club.
The roles were then reversed 12 minutes from time when the Argentine's fine through ball was clipped into the far corner by Torres.
Valencia's stuttering start to the season continued as they were held 0-0 at home to Real Betis.
Former Manchester United manager David Moyes is under increasing pressure as his Real Sociedad side are yet to win this season after a 3-2 defeat at home by Espanyol.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ