Goals from James Rodriguez and a second-half Robert Lewandowski penalty lifted Bayern to 12 points, two ahead of second-placed Hertha Berlin, who crushed Borussia Moenchengladbach 4-2 thanks to a Vedad Ibisevic double.
Pre-season title contenders Schalke have now lost all four Bundesliga matches and are anchored in last place.
"My team dominated for 90 minutes and allowed nothing in our own half," Bayern coach Niko Kovac told reporters.
"We created many chances but scored too few goals. But overall it was a great performance. We saw a really, really good Bundesliga game."
James put the visitors in front after eight minutes, powering his near-post header from a Joshua Kimmich corner past Schalke keeper Ralf Faehrmann.
David Alaba rattled Faehrmann's crossbar a little later with a curled free kick as Bayern kept up the pressure and Schalke, last season's runners-up, stayed toothless.
Pressure on coach Domenico Tedesco has been mounting for weeks following their disastrous start and he had a heated exchange with his player Franco di Santo after he was substituted.
"I am very angry because we had discussed it before the game," Tedesco said of Di Santo's substitution. "He was emotional. We will discuss this internally but it is only normal that I am disappointed by him."
James should have added another goal five minutes after the restart but somehow managed to fire wide in front of an open goal.
But he did make amends for his earlier miss when he earned a 64th-minute penalty which Lewandowski coolly converted.
Earlier, Borussia Dortmund's Christian Pulisic scored an 84th-minute equaliser to rescue a 1-1 draw at Hoffenheim.
The American, who got the winner at Club Bruges in a 1-0 Champions League group stage victory in midweek, tapped the ball home after good work from Marco Reus to earn his team a point.
Brazilian Joelinton had put the hosts ahead on the stroke of halftime and the visitors had Abdou Diallo sent off for a last-man foul on Andrej Kramaric.
But Pulisic timed his run to perfection to tap in Reus' cutback. Dortmund are third on eight points, two behind undefeated Hertha whose forward Ibisevic scored twice in their 4-3 win over Gladbach.
Werder Bremen, with 39-year-old striker Claudio Pizarro making his first start of the season, squandered a two-goal lead but still beat hosts Augbsburg 3-2 thanks to Davy Klaasen's 75th-minute winner after a goalkeeping error, to move up to fourth.
(Reporting by Karolos Grohmann; Editing by Ken Ferris and Ed Osmond)
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