The Brazilian registered three goals and his first Blancos minutes of the season in a comprehensive victory over Colombian outfit Millonarios.
The former World Player of the Year excelled in an 8-0 win for the Spanish champion against Millonarios, which Di Stefano scored 120 goals for between 1949 and 1953.
"Kaka has now shown that when well physically, he can be crucial to Real Madrid," the Brazilian's teammate Alvaro Morata, who scored two goals of his own, told reporters after the game.
Playing his first minutes of the season for Madrid, the attacking midfielder also finished the game with the captain's armband as well as the match ball.
"Kaka deserved the man of the match award after the game he played today," Morata added. "He gives me a lot of advice and I'm glad for his performance today."
Having played Rayo Vallecano just 48 hours earlier, many of the club's first-teamers, including Cristiano Ronaldo and Iker Casillas, watched the game from the stands. However, the likes of Benzema, Gonzalo Higuain and summer signing Luka Modric all featured.
The Colombian side has recently garnered exposure after it emerged that two of their league titles were won with the financial backing of drug lords.
Real Madrid hosts Deportivo La Coruna on Sunday as it aims to kick-start the defense of its league title after a poor start to the domestic season.
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