Thomas Muller and David Alaba gave Pep Guardiola’s men a two-goal cushion at the interval and, after surviving a series of scares, Robert Lewandowski struck twice after the break to keep Bayern on course for a third straight league title.
The champions have now scored 14 goals in eight days and, even without several first-team regulars, they proved again they are a cut above the rest of the division.
However, there was more frustration for Borussia Dortmund as they were held to a second successive goalless draw, this time by Cologne, to fall further off the European pace.
Dortmund did have the ball in the back of the net once, but that Pierre-Emerick Aubameyang effort was rightly ruled out for handball.
Schalke, who sit fifth, were also held to a draw, and needed a last-gasp equaliser from Joel Matip to get that much in a 2-2 draw at Hertha Berlin.
Anis Ben-Hatira gave the hosts the lead but debutant Leroy Sane scored an eye-catching equaliser for the Royal Blues.
Genki Haraguchi thought he had won it for the hosts but Matip struck late on to earn Roberto Di Matteo’s men a point.
Augsburg’s hopes of playing in Europe next season suffered a setback as they were beaten 2-0 at home by Mainz.
Shinji Okazaki put the visitors in front against the run of play and Augsburg were unable to make the most of their superiority, falling to a second goal from Koo Ja-cheol late on.
Defeat means Augsburg now only have a two-point advantage over seventh-placed Hoffenheim, who enjoyed a 3-0 win over 10-man Hamburg.
Eugen Polanski put Markus Gisdol’s men in front from the penalty spot after Jaroslav Drobny was given his marching orders midway through the first half.
Polanski added a second late on before Sebastian Rudy completed the scoring in a win which revives Hoffenheim’s hopes of playing in Europe next season while leaving Hamburg still on the brink of the bottom three.
Eintracht Frankfurt got back to winning ways after a heavy defeat in Cologne last week by dishing out a punishment of their own against Paderborn.
The prolific Alexander Meier opened the scoring in a 4-0 win with Marc Stendera and Stefan Aigner also on target to leave the East Westphalian side inside the bottom three.
Nelson Valdez, making his return after a six-month injury absence, put the cherry on top for the Eagles late on with his team’s fourth at the Waldstadion.