Real tied the last two league matches at the Santiago Bernabeu without goals, but started the match strongly and Kroos fired a powerful shot into the goal in the 14th minute after an effort from Marco Asensio on the right side.
Benzema, Real’s top scorer, added the second goal after David Alaba’s pass.
It seemed that Real would come out with a great victory until striker Radamel Falcao participated in the second half and quickly reduced the difference with a header, after the ball switched direction at defender Alaba, to deceive goalkeeper Thibaut Courtois in the 76th minute.
Rayo pressed in search of an equalizer, and Kroos kept the ball off the goal line after a defensive confusion, and Courtois saved a long shot from Unai Lopez.
Real’s tally of 27 points from 12 matches, two points behind second-placed Real Sociedad, who played the same number, but will regain the top if they beat Osasuna on Sunday.
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