After conceding six in the Champions League at home to Real Madrid in midweek, the last thing Schalke would have wanted was to be four goals behind after only 28 minutes.
David Alaba, Arjen Robben (2) and Mario Mandzukic put Bayern in control of the game before a charitable Rafinha own-goal gave Schalke some scant consolation.
Robben completed his hat-trick from the penalty spot after Kyriakos Papadopoulos was shown a red card on a day - and a week - to forget for Schalke.
Borussia Dortmund moved above Bayer Leverkusen into second place in the Bundesliga thanks to a 3-0 win over Nurnberg.
Mats Hummels and Robert Lewandowski's second-half goals put Jurgen Klopp's men on their way to three points before Henrikh Mkhitaryan made sure of victory in the 83rd minute.
With Leverkusen losing, Dortmund moved to second, but still a long way off runaway leaders Bayern Munich.
Leverkusen's miserable run of form continued as they lost their third-straight league game, going down 1-0 at home to Mainz.
Eric-Maxim Choupo-Moting's 27th-minute backheel was enough to earn Thomas Tuchel's men all three points and keep their hopes alive of playing in Europe next season, while denting Leverkusen's Champions League aspirations.
Werder Bremen took the honours in the 100th northern Germany derby against Hamburg, whose supposed revival ended after just one game with a 1-0 defeat at the Weser Stadion.
Zlatko Junuzovic decided matters in the 19th minute of a game which started with Bremen in dominating form, saw Hamburg recover for the start of the second half only to end with Bremen again in the ascendancy.
The result puts six points between the two sides with Hamburg stuck inside the bottom three in Mirko Slomka's second game in charge.
Augsburg and Hannover shared two goals at the Augsburg Arena, with the hosts missing an opportunity to move into the top six with a 1-1 draw.
Mame Diouf put Hannover in front against the run of play before Ragnar Klavan headed in an equaliser.
The Bavarians pushed for the win, which would have seen them move into a Europa League qualification berth, but Hannover held on to end their three-game losing streak and put six points between themselves and the bottom three.
Two extraordinary own goals, both by goalkeepers, ensured Eintracht Braunschweig and Borussia Monchengladbach took a point apiece from a 1-1 draw at the Eintracht Stadion.
Daniel Davari was first to turn the ball into his own net and give Gladbach the lead before the highly-rated Marc-Andre ter Stegen was left with egg on his face with an even worse error of his own gifting Braunschweig a point.