Second-place RB Leipzig suffered a shock loss to Mainz 05 on Saturday and Bayern took full advantage at the Veltins-Arena on Sunday, moving seven points clear at the top.
Schalke are bottom of the table with one win all season but they more than matched the European champions before Muller’s 33rd-minute breakthrough.
Muller doubled his tally late on after Lewandowski had scored his latest record-breaking goal early in the second half, before David Alaba added further gloss at the death.
The division’s leading scorer Lewandowski glanced over the crossbar from close range early on before a better chance came and went for Mark Uth, who headed straight at Manuel Neuer from five yards out.
Ralf Fahrmann was called into action with a fine double save to keep out Lewandowski’s free-kick and Serge Gnabry’s follow-up attempt.
Gnabry went close again when glancing the side-netting with a header he should have put away, but Bayern were in front seven minutes later through Muller’s powerful header.
The attacking midfielder met Joshua Kimmich’s back-post delivery and made no mistake in beating Fahrmann for his eighth league goal of the campaign.
Gnabry thought he had added a quickfire second after Leroy Sane’s initial effort was parried, only for the offside flag to go up against the former Schalke winger.
But the Bavarian giants did double their advantage early in the second period as Lewandowski controlled Kimmich’s long ball, held off two defenders and slotted under Fahrmann.
It is the 11th successive Bundesliga game in which Lewandowski has scored against Schalke and he nearly added another, dragging wide from 18 yards 20 minutes from time.
Schalke are now without a win against Bayern in 21 league matches and badly faded in the closing stages, with Muller heading in from another Kimmich delivery and Alaba adding a fourth with a 30-yard drive that squirmed under Fahrmann.
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