The in-form France striker took his tally to 16 in all competitions with the opener after 19 minutes, and also slotted home Real's fourth goal early in the second half before limping off with an ankle knock.
Levante stayed fourth but now have 30 points after being held to a 0-0 draw at home by Real Mallorca. Fifth-placed Osasuna also played out a goalless draw at Real Sociedad.
Malaga are sixth with 25 points after a 0-0 draw at home to Atletico Madrid on an uninspiring debut for the visitors' new coach, former Argentina captain Diego Simeone.
Atletico's Diego hit the bar in the first half but the hosts dominated in a game with more perspiration than inspiration.
Racing Santander spoiled Manolo Jimenez's debut as Real Zaragoza coach, winning 1-0 at home in the battle between the financially-troubled sides who started the day at the foot of the table.
Granada's first visit to the Bernabeu in 36 years got off to a bad start when Benzema, who scored the winner in the King's Cup in midweek, netted from Mesut Ozil's flicked pass.
"[Benzema's injury] doesn't seem to be serious," Real assistant coach Aitor Karanka told reporters, as he stood in for Mourinho who had to leave due to a family problem.
"He had a knock in the first half, and he came off as a precaution."
"Ronaldo is a professional and he was angry with himself, because things weren't coming off well for him," Karanka added. "We know how keen he is to try and help out the team."
