With Cristiano Ronaldo relatively subdued by his high standards, France striker Benzema scored a superb goal and created two more as Los Merengues ran riot against the Basques.
Sergio Ramos, Mesut Ozil and Sami Khedira were also on target, with Real's 12th-minute opener an own-goal from defender Jon Aurtenetxe, who sent Benzema's shot past his own keeper.
Ibai Gomez was on target for the visitors, who sit 12th after the defeat. Real are in third but lie eight points shy of leaders Barcelona, who beat Real Zaragoza 3-1.
Real have now put 19 goals past Bilbao in their last four league meetings at the Bernabeu and the big surprise of the night was that Cristiano Ronaldo failed to add to his 12 La Liga goals this term.
The former Manchester United forward returned to action after suffering a gash above his left eye in last weekend's 2-1 win at Levante that forced his withdrawal from the Portugal squad to play in Gabon midweek.