The Frenchman's brace came either side of a maiden senior league goal for defender Alvaro Odriozola, as Real moved onto 70 points, level with city rivals Atletico Madrid, who have a game in hand, but top due to their better head-to-head record.
"We started the game really well, robbing the ball high, that was the gameplan," Madrid defender Marcelo said.
"We know there are no easy games in La Liga, it might have seemed like an easy win, but we were really good.
"Madrid never give up. We'll fight [for the title] until the end in every game we have."
The home side, who were looking to complete an unlikely league double over Madrid, started brightly, with Jens Jonsson firing narrowly wide, however that was as good as it got as Real's class told.
Benzema netted his first from the penalty spot on the half hour following a VAR intervention, which spotted an Isaac Carcelen foul on Vinicius that referee Antonio Mateu Lahoz had missed.
The striker's goal took him level with club great Raul Gonzalez as having scored against 35 different opponents in La Liga.
He turned provider three minutes later when he crossed for Odriozola.
Casemiro should have made it 3-0 moments later when he fired over from close range, however five minutes before the break he crossed for Benzema, who completed his double to seal the points for Zinedine Zidane's side.