Niklas Sule, Leon Goretzka and Douglas Costa returned from the Bayern side that overcame Mainz, as Gladbach were without Marcus Thuram and Alassane Plea.
It was all Bayern following the opening exchanges, as Gladbach sat back with the hope of getting a chance on the counter-attack in a tightly contested spell.
An outstretched hand from Florian Neuhaus following a ball from Alphonso Davies gave Bayern a penalty on 20 minutes, leaving Robert Lewandowski to net the opener.
It was two goals six minutes thereafter when a powerful finish by Goretzka from 20 yards fizzled beyond the reach of Gladbach goalkeeper Yann Sommer.
Gladbach pulled a goal back ten minutes before halftime as Jonas Hofmann sent a low finish past Manuel Neuer from a through ball by Lars Stindl.
Hofmann made it all square with the last kick of the first half after he raced onto a ball into space from Stindl to beat Neuer, with calls for offside dismissed by the Video Assistant Referee (VAR).
As neither side made changes during the break, Gladbach went ahead on 49 minutes after a ball from the left-side found Neuhaus who blasted into the top corner.
Bayern struggled to get any openings towards the midway stage in the second half, with a speculative shot from Leroy Sane and half-hearted volley from Lewandowski the closest it got for them.
This led Hansi Flick to look to his substitutes bench inside the final 20 minutes and called on the services of Kingsley Coman, who came on for Costa.
However, Gladbach maintained resistance as Sule saw his attempt from the far post cleared off the goal-line from Matthias Ginter as the hosts held no for a famous win.