It was the 16th straight league win for Madrid, going back to last season, matching Pep Guardiola's Barcelona in the 2010-11 season.
Madrid maintained a three-point lead over Barcelona with its fourth straight league victory this season.
Celta Vigo and Valencia remained winless, while Villarreal stayed near the top thanks to a spectacular goal from near the halfway line by Italian striker Nicola Sansone.
Madrid's victory came despite the absence of Cristiano Ronaldo and Gareth Bale, who were rested by coach Zinedine Zidane.
Madrid is the only team to have won four straight to start the league. Barcelona won 5-1 at Leganes on Saturday to rebound from a 2-1 home loss to Alaves a week ago. Atletico Madrid routed Sporting Gijon 5-0 to win its second consecutive match and reach eight points, behind third-place Las Palmas, the league's early surprise team.
Rodriguez opened the scoring by converting a penalty kick in first-half injury time and Benzema sealed the away victory from close range in the 71st minute.
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