Real, who were missing eight players due to a COVID-19 outbreak in the club, stretched their unbeaten run to 15 matches in all competitions as they reached the mid-season break with 46 points, eight clear of Sevilla and 13 ahead of third-placed Betis. Athletic remain 10th with 24 points.
Benzema broke the 400-goal mark in his professional career with a stunning strike from just outside the box in the fourth minute before adding another just three minutes later when an Athletic defender missed a clearance.
Oihan Sancet stopped Real's momentum with a sensational goal in the 10th minute.
The hosts put up a fight but Real held on to secure all three points.