Madrid went ahead through Vinicius Junior in the 47th minute -- substitute Luka Jovic, who had earlier replaced Benzema, with the assist -- before Jovic doubled their lead ten minutes later with an instinctive close-range header.
Benzema will undergo tests in the coming days to determine the extent of his injury ahead of a week which will see Madrid face Inter Milan in the Champions League before a LaLiga derby with title rivals Atletico Madrid next weekend.
Saturday's match at the Reale Arena began with a blow for Madrid as Benzema, 33 -- who's the top goal scorer and assist provider in Spain this season -- was taken off in the 17th minute, complaining of discomfort.
"Karim had a problem in the first half, he felt a bit of discomfort, he didn't want to force it," Real coach Carlo Ancelotti said. "We'll see in the next few days, I don't think he'll be available for Tuesday's game [vs. Inter Milan] but he could be for Sunday [vs. Atletico Madrid]."
Madrid continued to push forward, though, and Vinicius Junior, Rodrygo and Luka Modric all tested goalkeeper Alex Remiro before defender Igor Zubeldia was booked for bringing down Vinicius on the edge of the box.
Eder Militao made an athletic block to prevent forward Alexander Isak getting a shot on goal, and Madrid were almost caught out on the counter when a Toni Kroos free kick routine went wrong before half time. The visitors went ahead not long after the interval.
Jovic received the ball from Vinicius and laid it off for the Brazil international to slot home his tenth league goal of the season.
Their confidence buoyed, Madrid made it 2-0 in the 57th minute. Kroos' corner was headed goalwards by Casemiro, and Jovic pounced to glance another header past Remiro. It was only the Serbia forward's third goal for Real Madrid since his €60 million signing in 2019, and his first since February 2020.
Another substitute, Eduardo Camavinga, was required to execute an expertly timed slide tackle on Isak inside the penalty area as La Real pushed for a foothold in the game. As the game opened up in the final minutes Militao played Vinicius through on goal, but he was denied this time by Remiro.
"We made a complete game," Ancelotti said. "Ball control, defence, between lines, the positional game... What I like the most is that this team knows how to defend. I never doubted the men up front but the commitment shown in defence is very good.