Luis Suarez gave Barcelona the lead in a game which appeared to be heading to a draw before Lionel Messi sealed the victory with the second to hand the Catalan giants a win at Villarreal on Sunday in the La Liga.
The five-time Ballon d'Or winner struck seven minutes from time to double Barca's lead as he collected the ball outside the box and went on a run before slotting past Villarreal goalkeeper Sergio Asenjo.
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Muller scored 525 goals in 572 appearances for Bayern Munich between 1965 and 1979, a record which had stood for almost 40 years.
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Messi, who previously broke Muller's record of goals in a calendar year when he netted 86 times during 2012, has scored 525 goals in 605 games for Barcelona.