Benzema tapped in Sergio Reguilon's cross on the half hour but Real had to wait until the final 10 minutes to seal their fourth successive league win to leave them eight points adrift of leaders Barcelona.
Vinicius Junior started and finished a counter attack to double the lead 2-0 and substitute Mariano Diaz headed in a late third.
Real coach Santiago Solari said, "We are going to fight for everything, always, until the end, hopefully until the end of the calendar, it will mean that we have reached the finals.
"But today there has been hunger to cut points.
"Madrid never gives up, we show that hunger to cut, as in every day. We always go out to win, beyond mathematics."
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