Pep Guardiola's men were held to a 0-0 draw by Shakhtar Donetsk in the first leg of their UEFA Champions League last 16 tie on Tuesday, though they were back to their ruthless best at the Benteler Arena, following up last week's 8-0 thrashing of Hamburg impressively.
Robert Lewandowski marked his recall to the starting XI, in place of Mario Gotze, with two goals in a first half of few chances.
However, Bayern picked off the hosts almost at will following the dismissal of Florian Hartherz in the 62nd minute, Arjen Robben netting either side of Franck Ribery and substitute Mitchell Weiser also finding the net, putting the champions 11 points clear at the top.
Leverkusen missed out on the chance to go above fourth-placed Schalke, as they were held to a dramatic 2-2 draw by fellow European hopefuls Augsburg.
Following a 5-4 home defeat by Wolfsburg last time out, coach Roger Schmidt revealed that he would be making changes to his team and that approach paid off after just eight minutes, as Josip Drmic – in for the dropped Stefan Kiessling – put the visitors ahead.
Although half-time substitute Caiuby levelled for the hosts just before the hour mark, Stefan Reinartz struck six minutes from time to seemingly hand Leverkusen a valuable away win.
But Augsburg keeper Hitz stabbed home in the fourth minute of stoppage time, leaving the two teams side-by-side in the Bundesliga table.
Schalke retained their place in the final UEFA Champions League place despite drawing 1-1 at home to in-form Werder Bremen, who rescued a point thanks to Sebastian Prodl's equaliser just before the end.
Martin Schmidt's start to life as Mainz coach began in fine fashion, as his men beat local rivals Eintracht Frankfurt 3-1 in the Rhine-Main derby, with Carlos Zambrano's late red card compounding a disappointing day for the visitors.
Hannover left Koln with a 1-1 draw in spite of Joao Pereira's red card at the death, while towards the wrong end of the table, Freiburg moved out of the bottom two thanks to a 1-1 draw at home to Hoffenheim.
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