Rafael Benitez's side came into the match unbeaten in the league and having scored 15 goals in their last three matches and they dominated proceedings throughout the match, although Granada could have opened the scoring when Isaac Success just could not reach Edgar Mendez's whipped cross.
Real had their first big opportunity of the match after 20 minutes when Benzema slid a pass in to Cristiano Ronaldo, but the Portuguese was denied a ninth goal in three games by a smart low save from Andres Fernandez.
© Getty Images
Within a minute, Granada had the ball in the net at the other end but they were harshly denied a shock lead when Youssef El-Arabi was adjudged to have been offside when he converted Success's low cross.
Ronaldo was denied by Andres again before the goalkeeper spread himself to prevent Benzema scoring from Isco's fine pass as Real looked to take advantage of that let-off, and the visiting stopper pulled off his best save of the lot to deny Luka Modric from close range just before the break.
© Getty Images
Granada had a golden opportunity to go in front within seven minutes of the restart when El-Arabi's flick sent Success through on goal but the attacker's effort dropped wide Keylor Navas's post.
The away team were made to pay for that waste almost instantly as Benzema finally broke Andres's resistance, heading Isco's cross home to give the hosts the lead.
El-Arabi was denied by a save from Navas as Granada refused to fold, but Benitez's side missed chances to kill the game off late on through Ronaldo and Denis Cheryshev as the visitors just could not reward their impressive display with a point.