Bayern targeted a positive start to their title defence and awarded new signing Dayot Upamecano a debut, as new Gladbach manager Adi Hutter preferred Alassane Plea to lead their attack.
Plea made his presence felt in no less than ten minutes when he helped a snap delivery from Lars Stindl past Bayern goalkeeper Manuel Neuer after the visitors battled to clear their defensive lines.
The reigning champions weren't prepared to throw in the towel and instantly went searching for the equaliser through a first-time volley by Robert Lewandowski, but goalkeeper Yann Sommer saved.
Lewandowski was presented another opening shortly before the half-hour mark through a cross from Alphonso Davies, but Sommer once again thwarted the Polish international.
There was no stopping the record-breaking marksman four minutes from halftime as he escaped his marker in the area to go on and volley a corner-kick from Joshua Kimmich past Sommer.
Lewandowski continued to pose a threat seven minutes following the restart through a snap header from a cross by Leroy Sane, but Sommer was able to deal with the danger.
The Gladbach keeper still frustrated the champions later on when his outstretched leg from a ball by Serge Gnabry denied Davies before an identical block denied Lewandowski a certain goal.
As the momentum shifted, Neuer tipped a low strike from Stindl away seconds from substitute Marcus Thuram missing a sitter off a ball across the face of goal.
Bayern threw on a double change in the last 15 minutes in Jamal Musiala for Gnabry and Kingsley Coman ahead of Sane.
There were no further threats though from either side as they ran down the closing stages to play to a 1-1 draw on the opening day in the Bundesliga.