He scored his 14th La liga goal in the 3-0 win over Cadiz on Sunday.
Jude Bellingham scored his 14th goal of the season as Real Madrid returned to the top of La Liga with a 3-0 victory at lowly Cadiz.
He now has the most goals by any Real Madrid player in their first 15 games.
The previous record of 13 was jointly held by Cristiano Ronaldo, Alfredo di Stefano and Pruden.
England midfielder Bellingham has 11 goals in 12 La Liga games and three in the Champions League since joining from Borussia Dortmund in the summer.
Real went into the game two points behind Girona and took an early lead through Br azil forward Rodrygo.
The 22-year-old then doubled Real's lead midway through the second half.
Bellingham, 20, then continued his remarkable start to life in Madrid by firing home to seal Real's third straight win.
The Birmingham City youth product had a hand in the first goal, playing it wide to Rodrygo, who appeared to have run into a dead end inside the penalty area but managed to maintain possession and fire into the top corner.
Real lost forward Vinicius Jr to injury during the international break but fellow Br azilian Rodrygo has now scored in three straight games for Real for the first time since joining from Santos in 2019.
Luka Modric drilled a low strike against the foot of the post in the second half and moments later helped the ball on to Rodrygo, who cut inside before firing inside the far post.
Rodrygo then laid off to Bellingham in the left channel and the in-form Englishman fired a fine left-footed strike across goal and into the bottom corner.