The runaway leaders – now 48 matches unbeaten in the league – completed a miserable week for Schalke, hammered 6-1 in the UEFA Champions League by Real Madrid on Wednesday, as Robben scored three times and David Alaba and Mario Mandzukic also netted.
Bayern were rampant throughout at the Allianz Arena and it took the reigning champions just three minutes to break the deadlock.
Alaba's free-kick from just outside the Schalke penalty area took a massive deflection to give goalkeeper Ralf Fahrmann no chance.
Mandzukic headed in his 14th league goal of the season either side of Robben's double
Bayern now sit 20 points clear of second-placed Borussia Dortmund as Pep Guardiola's men attempt to finish the Bundesliga season unbeaten.
Guardiola's team made the perfect start as the home side took a fortuitous lead after just three minutes.
Mandzukic added a third goal after 24 minutes as he leapt between two defenders and met Alaba's fantastic cross from the left with a thumping header.
Robben was a constant threat and he grabbed his second and Bayern's fourth four minutes later, when he latched on to Rafinha's header on the right side of the penalty area and curled a shot into the bottom-left corner.
Fahrmann stopped Mandzukic from adding a fifth from close range with a great save with his outstretched left foot on 37 minutes. At the other end, Manuel Neuer continued Schalke's misery, making a world-class save off a Christian Fuchs shot just before the break.
