Benzema reach the 21league goals this season, including 10 goals in his last seven appearances forthe club.
The victory left Real Madrid, who had drawn with Leganes in their last outing, in third place on 64 points. They are 13 points behind leaders Barcelona and four behind city rivals Atletico.
Zinedine Zidane once again left Gareth Bale on the bench,with Lucas Vazquez and Marco Asensio supporting Benzema in attack.
They initially cut frustrated figures throughout an openingperiod of few chances, with the Bernabeu crowd voicing their frustration.
However, the fans were soon serenading Benzema two minutesafter the break when he opened the scoring.
Benzema doubled thescore 15 minutes from the end, heading in Luka Modric's corner after acalamitous misjudgement from Bilbao goalkeeper Iago Herrerin.
The Frenchman completed his hat-trick by firing into anempty net during the injury time.