Benzema linked with Rodrygo before slotting home from 18 yards, having seen two earlier efforts ruled out by the Video Assistant Referee.
That doubled Madrid's lead after Federico Valverde sliced home.
Marco Asensio scored a third as Real extended their unbeaten start to 10 games.
It left Benzema to celebrate his fifth league goal of the season by ironically drawing a square like the referee does during a VAR review.
Asensio's hooked finish rounded off a lovely free-flowing move by Real, who have won nine and drawn one as they seek to retain their league title.
They have won their first six away league games for only the second time, after the 1991/92 campaign.