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.
Fit-again Robben, recently back following a knee injury, helped himself to first-half brace, his first a lovely chip from close range before doubling his tally thanks to a curling shot into the bottom-left corner.
Mandzukic headed in his 14th league goal of the season either side of Robben's double
Schalke managed to snatch a consolation goal after the hour mark when a corner resulted in Rafinha turning it into his own net before Robben claimed the match ball with his third from the penalty spot after Kyriakos Papadopoulos had upended Mandzukic as the last man, which resulted in a red card.
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.
Rafinha was fouled on the edge of the box after a great run from Robben and the subsequent free-kick from Alaba took a wicked deflection off the wall to loop over Fahrmann in the Schalke goal.
Bayern continued to pressure the away side in the early stages and were rewarded with a second after 15 minutes.
Robben was played through by Bastian Schweinsteiger and finished off with a delicate chip over the diving Fahrmann.
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.
The Netherlands international almost completed a quick-fire treble when he cut in from the right and unleashed another curling effort, but his shot down sailed over.
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.
Schalke grabbed one back after 62 minutes when a corner was turned in by Bayern defender Rafinha for an own goal.
Papadopoulos was then dismissed for tangling with Mandzukic in the area as the last man and Robben slammed the spot-kick into the top-left corner.
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