Even without the injured Cristiano Ronaldo, Real were far too strong for Racing and Jose Mourinho's side responded with their eighth league away win of the campaign to close in on Barcelona, who had defeated Real Zaragoza 1-0 on Saturday.
Real had crushed Malaga 7-0 on Thursday and it could have been a similar scoreline in a dominant first half against Racing as they dominated from the get-go.
Xabi Alonso hit the crossbar in the 12th minute with what seemed to be an overhit cross and two minutes later Brazilian Marcelo missed a sitter.
Marcelo's late run into the box was picked out and the left back rounded the goalkeeper, but somehow sliced wide of goal when he had done all the hard work.
Benzema then thumped the crossbar with a fierce drive before Real produced a fantastic team goal on 23 minutes with some slick one-touch passing.
Alonso fed German international Ozil who began an exchange of quick passes with Togo forward Emmanuel Adebayor and Benzema, before putting the ball on a plate for Adebayor to roll home his second league goal of the campaign.
Three minutes later Ozil found Benzema with a brilliant pass and the Frenchman took the ball in his stride before slotting home.
Racing had a chance to get a foothold in the match when Alonso conceded a penalty six minutes after the interval, but Pablo Pinillos took an awful penalty that goalkeeper Iker Casillas held comfortably.
Real went off the boil in the second half and Racing pulled a goal back in the 69th minute with Swedish midfielder Kennedy Bakircioglu making a clever run to steal a yard on the defence and then finish past Casillas.
Real were in for a nervy final 20 minutes but Benzema ensured that didn't happen by scoring his second three minutes later after a fine pass from Angel di Maria.
With Ronaldo missing, Adebayor was entrusted with taking a late penalty and failed miserably with a poor spot-kick to rival that of Pinillos.
In other matches, Athletic Bilbao ended a run of four league losses with a vital 2-0 home win over European rivals Sevilla at San Mames on Sunday.
A disastrous own goal from Argentine centre-back Federico Fazio on 66 minutes put Bilbao ahead before Andoni Iraola converted an 88th minute penalty after French defender Julien Escude committed a needless foul.
Bilbao moved a point above Espanyol, who lost 1-0 at promoted Levante on Sunday, into fifth place.
Sevilla, fourth last season, trail Bilbao by three points along with Atletico Madrid as a host of teams tussle for a top six finish.
Sevilla coach Gregorio Manzano had warned of the threat from Bilbao's striker Fernando Llorente and the Spanish international almost scored in the fifth minute with goalkeeper Javi Varas stopping his header.
Varas was then called upon to stop a header from Javi Martinez on 23 minutes as hosts Bilbao started the stronger.
It took a mistake after 66 minutes to open up the game with Fazio getting his feet in a tangle as he tried to clear a whipped-in cross from the left and the Argentine deflected the ball into his own net.
Escude gifted Bilbao the second goal they craved with a reckless tackle in the penalty area two minutes from time and Iraola struck the penalty to clinch the points.
Earlier Almeria moved off the bottom with two goals in three minutes sealing a comeback 2-1 win at relegation rivals Hercules on Sunday.
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