Benzema latched onto the ball following some poor control from Cristiano Ronaldo to fire low past Roberto and score the only goal of the game in the 10th minute.
But the hosts will feel they should have had a late penalty kick for a Casemiro challenge on Diego Buonanotte.
Carlo Ancelotti again left Iker Casillas on the bench, with Diego Lopez taking his place in goal. Angel Di Maria, Mesut Ozil and Benzema all started for Real who were looking to keep up with the early pacesetters in La Liga.
The early signs were that Real would run away with the match as Ancelotti’s side quickly took the initiative.
The lively Di Maria slid the ball in for Benzema who lobbed it over the goalkeeper but out for a goal kick.
Real did not have to wait long to take the lead as Di Maria curled the ball in from the right, Ronaldo mis-controlled, but the ball rolled into the path of Benzema who fired home left-footed beyond Roberto.
Ozil thought he had given his side a 2-0 lead after 14 minutes when he ran onto a long free-kick from Di Maria and lobbed sublimely over Roberto. However, play was pulled back as the ball was moving when Di Maria took the free-kick.
Granada spurned a great chance to go level as Youssef El-Arabi found himself one-on-one with Diego Lopez who kept his nerve and saved what was ultimately a tame shot from the striker.
Benzema left an Alvaro Arbeloa cross to Ronaldo who made a hash of his shot before falling unceremoniously to the floor. It was a presentable opportunity for Ronaldo on the edge of the six-yard box.
Granada grew in confidence as the half progressed, with Marcelo and Pepe both going into the book as the Real defence was put under increasing pressure.
Sergio Ramos got his head onto an Ozil corner early in the second-half and Roberto initially fumbled before claiming the ball at the second attempt.
Isco skipped around Manuel Iturra and Roberto did well to get his right hand on the shot and deflect it onto the post.
Benzema passed up a presentable opportunity as he ran onto a through ball and shot wide of the near post.
This was a stuttering Real Madrid performance, although they were largely dominant in the final 20 minutes as Ronaldo, in particular, came to life.
The Portuguese attacker reacted quickly to head the ball beyond Pape Diakhate and fired in a low shot that Roberto managed to hold.
Ronaldo then cut in from the left and let fly with a powerful shot that Roberto punched away.
The game’s pivotal moment came in the 83rd minute when substitute Buonanotte went down under a challenge from Casemiro. The Brazilian youngster did not get anything on the ball but the referee waved play-on, much to the relief of the Real Madrid players.
Pepe made an invaluable clearance on a dangerous low cross from Piti as Granada ended the match strongly but Real held on to make it two wins in two games.