He moved one ahead of Alfredo di Stefano's tally of 307 when Sergio Ramos crossed from the right after 15 minutes at the Molinon and Raul caught the ball with a first time shot on the half-volley.
He grabbed his 309th goal, and Real's fourth on the day, when Inaki Lafuente fumbled Gonzalo Higuain's shot leaving Raul with a simple tap in near the end.
"Many years are going to pass before there is another player like Raul," Real coach Juande Ramos said after the game.
"He's always leading from the front, giving his all, taking responsibility in the team and all that remains for me is to congratulate him."
Raul scored his first for the nine-times European champions against city rivals Atletico Madrid in November 1994 aged 17.
His total includes 216 in the league, 18 in the King's Cup and he is the Champions League's leading scorer with 64. The remainder were scored in other tournaments.
The 31-year-old number seven has won three European Cups and six league championships and is now in his 15th season with Real. He also played 102 times for Spain between 1996 and 2006, scoring a record 44 goals.
Argentina-born Di Stefano helped Real to five consecutive European Cups between 1956 and 1960, and won eight league titles. He was made the club's honorary president in 2000.
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
