The Gelsenkirchen club has now conceded 11 goals in a week after the Netherlands winger scored three times in a demolition job at the Allianz Arena
The runaway leaders – now 48 matches unbeaten in the league – completed a miserable week for Schalke, hammered 6-1 in the Champions League by Real Madrid on Wednesday, as Robben scored three times and David Alaba and Mario Mandzukic also netted.Bayern now sits 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 Ralf Fahrmann in the Schalke goal.
Bayern continued to pressure the away side in the early stages and was 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 after cutting in from the right and unleashing another curling effort, but his shot 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 did pull one back on 62 minutes when a corner was turned in by Bayern defender Rafinha for an own goal, but Kyriakos Papadopoulos was then dismissed for tangling with Mandzukic in the area.
The Greek international was shown a straight red card as the last man and Robben slammed the spot-kick into the top-left corner to complete the rout.