Goals from Leroy Sane, Jamal Musiala and Sadio Mane all before the interval put the champion firmly in the driving seat for a deserved victory at Allianz Arena before Thomas Muller added a fourth close to full-time.
After a dismal domestic run saw it go four league games without a win, questions had been asked about Julian Nagelsmann's side and its purported chances of claiming another top-flight crown.
But for now, they have been emphatically silenced, while Gerardo Seoane's side saw its horror-show start to the campaign worsened in painful fashion on the road.
It took Sane just three minutes to split open the visitors, fed off the right wing and able to roll a deflected strike beyond the wrong-footed Lukas Hradecky.
Musiala followed suit just after the quarter-hour mark, playing a one-two with Muller off a long ball before squeezing a shot in, and Sane added a third from the edge of the box six minutes from the break.
Mane saw a second overturned 10 minutes after the interval when the video assistant referee (VAR) deemed Odilon Kossounou to have been fouled, but that call was likely scant consolation for Leverkusen.
Yet Bayern was not done, and when Muller pressed Hradecky late on, a tragicomic slip from the goalkeeper left an open net for the veteran to turn home and round off a comprehensive win.