Luis Enrique's men have now gone 35 matches without defeat across all competitions, bettering the streak Los Blancos managed under Leo Beenhakker in the 1988-89 season.
Barcelona has now gone 35 matches unbeaten in all competitions after claiming victory over Rayo Vallecano on Thursday evening, setting a new Spanish record in the process.
The Catalan giants, who top the Liga table, tied Real Madrid's long-standing record on Sunday courtesy of a 2-1 win over Sevilla at Camp Nou, but have now gone one better by extending their streak even further.
Los Blancos had held the record since the 1988-89 season, when Leo Beenhakker's Madrid side – which featured the likes of Hugo Sanchez and Emilio Butragueno – notched 25 wins and nine draws, but Barcelona has improved on those figures with 29 victories and six draws.