Robert Lewandowski carved his name in history with a double for Bayern Munich, while Schalke drew level with Dortmund.
Dortmund lost ground on Bayern Munich at the top of the Bundesliga on as they dropped points for the first time this season.
Borussia Dortmund returned to the top of the Bundesliga with a 3-0 victory over Bayer Leverkusen on Sunday.
Thomas Muller struck twice as Bayern Munich beat Bayer Leverkusen 3-0 in the Bundesliga on Saturday, as Eintracht Frankfurt thrashed Stuttgart 4-1.
Manchester City ended an indifferent pre-season campaign with a heavy 4-2 defeat away to Stuttgart on Saturday.
Stuttgart have announced two new signings as they look to avoid a second consecutive relegation battle.