Benzema and Toni Kroos were on target to help Real Madrid defeat Athletic Club.
A goal in either half helped Real Madrid defeat Athletic Club 2-0
Real Madrid travelled to San Mames buoyed by their comeback victory over Villarreal in the Copa del Rey, and the defending champions beat Athletic Club to close the gap on league leaders Barcelona.
Real Madrid's early pressure was rewarded in the 24th minute when Marcos Asensio found talisman Benzema, who finished brilliantly to put Los Blancos ahead.
Athletic Club thought they equalised in the 78th minute, but the VAR confirmed the linesman's call, and the goal was ruled out for offside.
Toni Kroos sealed Madrid's victory with a brilliant strike in the 90th minute.
The win puts them back in the three-point range behind Barcelona, while Athletic Club misses out on finishing the gameweek in European competition qualifying spots, remaining eighth.
Real Madrid roar past the Lions
The home side started better, but it was Real Madrid who got the first goal after Marco Asensio's lofted header into the box was connected with by Benzema, who struck the ball on a volley with his weaker foot past the stunned Unai Simon in goal for the Basque club.
Athletic Club, despite their uninspiring performance in large parts of the game, finally put the ball across the goal line.
Inaki Williams strikes home from close range after Courtois parried a shot resulting from a corner into his path, however, the ball struck a Bilbao player in an offside position before the ball reached Courtois.
Real Madrid sealed their victory in the final moments of the game, as Toni Kroos struck the ball so expertly into the corner of the net.
Real Madrid chase Barcelona
Anything but maximum points would have meant Barcelona kept a healthier lead against their rivals, Real Madrid.
Barcelona extended the lead to six before Madrid played, beating Getafe 1-0, but the defending champions took the pressure well and responded with a victory against one of the better teams in the league.