Robert Lewandowski scored his fourth goal in three games from the penalty spot to get the champions off the mark before James Rodriguez – making his first Bundesliga start – doubled their lead.
Rodriguez turned creator for Bayern's third, providing a brilliant assist for second-half substitute Arturo Vidal to open his account for 2017-18.
Ancelotti came under fire after Bayern were beaten 2-0 by Hoffenheim in their third game of the Bundesliga season 10 days ago, but there were few signs of a repeat result at Veltins Arena.
The two sides went into the game level on points and with victories from their previous two games but Schalke struggled to contain Bayern's attack despite the absence of Arjen Robben, who missed the game through illness.
The visitors also lined up without injured goalkeeper Manuel Neuer, although deputy Sven Ulreich impressed when called upon to ensure three points went back to Bavaria.
Bayern peppered Ralf Fahrmann's goal with shots from the outset and the Schalke keeper made an excellent save after seven minutes to keep out Sebastian Rudy's fierce drive, before thwarting Thomas Muller at close quarters.
Guido Burgstaller had the ball in the net in the 21st minute when Schalke swept through the Bayern defence, converting following a double save from Ulreich, but the offside flag was raised.
That disappointment was compounded for the home side two minutes later when Naldo was judged to have blocked James' cross with his arm.
Marco Fritz consulted his video assistant referee before pointing to the spot and Lewandowski made no mistake from 12 yards, sending Fahrmann the wrong way to score in the bottom left corner.
Bayern were gifted an easy second when Corentin Tolisso squared to James, who found himself completely unmarked on the edge of the box and beat Fahrmann with a low shot at his near post to make it 2-0 after 28 minutes.
Muller crashed a header against the post from James' cross five minutes into the second half, before Leon Goretzka muscled his way through the Bayern defence and flashed a shot narrowly wide at the other end.
Schalke continued to probe for a way back into the game and substitute Yevhen Konoplyanka burst into the box before dragging a shot across the face of goal and wide of the far post, before Goretzka missed with an ambitious low drive from 25 yards.
Burgstaller should have made it 2-1 when he went one-on-one with Ulreich after 65 minutes and shot straight at the goalkeeper's feet, but 10 minutes later the game was put out of Schalke's reach.
Bayern's third goal was superbly crafted by the ever-industrious James, who turned three defenders on the edge of the Schalke penalty area before playing a wonderfully delicate chip to Vidal and the Chilean thumped the ball into the top corner with aplomb.
Rodriguez almost capped a brilliant full Bundesliga debut with a second goal when he met Muller's cross with a first-time shot from close range, but Fahrmann turned it around the post to prevent a more emphatic scoreline.
Key Opta stats
- Robert Lewandowski has been involved in nine goals (seven scored and two assists) in his last five competitive games against Schalke (four Bundesliga, one DFB-Pokal). He scored in each of these games – currently his longest run against an opponent.
- Arturo Vidal has won his last 11 Bundesliga games when scoring (nine for Bayern, two for Leverkusen) – a run that started after Leverkusen’s 2-2 against Freiburg in December 2010.
- Since a 2-0 home win in December 2010 Schalke have not won any of their last 14 Bundesliga games against Bayern (three draws, 11 losses). In their Bundesliga history they only once had such a long run against an opponent – also against Bayern. That slump lasted 17 games and 11 years between October 1984 and December 1995.
- Bayern have not lost any of their last 24 Bundesliga games during the Oktoberfest (20 wins, four draws) – the last loss was on October 3 2010, 2-0 at Borussia Dortmund.
- Lewandowski scored his 157th Bundesliga goal and is now level up with Stuttgart legend Fritz Walter in 13th on the all-time list.