After scraping past Real Valladolid on Wednesday evening, Zinedine Zidane opted to stay with Vinicius alongside Benzema.
Vinicius got the breakthrough on 16 minutes for the defending champions with a superb finish past Aitor Fernandez with Luka Modric picking up the assist.
The woodwork then came to Los Blancos' on the stroke of halftime as Benzema saw his effort clip the upright.
Much like the first half, Real dominated coming out from the break as both Vinicius and Benzema had a couple sights at goal in the opening 15 minutes.
Zidane's men did have the ball in the back of the net in the 70th minute through Sergio Ramos' header, but the goal was disallowed for a foul in the build-up.
Nevertheless, Benzema ended any hopes of Leganes comeback late in the game with his second league goal of the campaign.