Luis Suarez scored twice, while Neymar and Andres Iniesta also scored as Barcelona moved six points clear of Real at the top of the table.
BBC Sport reviews each player's performance, with BBC Radio 5 live co-commentator Chris Waddle, who was at the Bernabeu, giving his ratings out of 10.
Barcelona took the honours in the first El Clasico of the La Liga season with a dominant 4-0 win at Real Madrid on Saturday.