Messi struck twice in the victory over Real Mallorca, to take him past the Brazilian great who scored 75 in 1958 for Santos and Brazil.
Messi is now nine behind German star Muller, who has the all time record with Bayern Munich and West Germany from 1972.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.