Benzema converted Marcelo’s left-wing cross after 27 minutes to move the hosts on to 12 points in Group B and book their place in the knockout phase, while Liverpool remain third on three points.
Liverpool manager Brendan Rodgers sprang a surprise by making seven changes, leaving out Steven Gerrard, Raheem Sterling, Jordan Henderson, Mario Balotelli, Philippe Coutinho and Glen Johnson from his starting line-up and selecting instead the likes of Lazar Markovic, Javier Manquillo, Fabio Borini, Emre Can and Adam Lallana.
But rather than collapse against the defending European champions, the inexperienced side fought valiantly throughout the game, without ever really threatening an equaliser.
Liverpool started confidently but could have gone behind after four minutes, when James Rodriguez was afforded space on the edge of the box and drew a desperate save from Simon Mignolet with a curling left-foot shot.
The Belgian produced another magnificent stop six minutes later, after Benzema dispossessed Martin Skrtel in the box and fed Cristiano Ronaldo, whose fierce drive was tipped over.
Real subsequently took control on both possession and territory, but with Kolo Toure outstanding in defence and Lucas protecting the back line vigilantly, they were unable to break through.
However, Marcelo then received the ball in space after 27 minutes and swept in a brilliant cross behind the Liverpool defence to the back post, where Benzema stretched unmarked to divert the ball into the roof of the net.
Bale hits bar
It looked like Liverpool would struggle to keep it at 1-0 until half-time, but the excellent Mignolet came to the rescue twice more with fine stops to deny rasping strikes from Ronaldo and then Marcelo.
Mignolet thwarted Ronaldo once more four minutes after the break, but then Liverpool grew in stature as Rodgers began to commit men forward, with Alberto Moreno seeing a left-foot strike saved by Iker Casillas, before Adam Lallana sent a shot flashing across goal.
Rodgers looked to build on the momentum by sending on Gerrard, Sterling and later Countinho, but the changes instead halted their progress and Real duly regained the upper hand.
Benzema diverted another Marcelo cross narrowly over and second-half substitute Gareth Bale then rattled the bar from another Marcelo centre, but despite late pressure from Liverpool, the single goal proved enough.