In sharp contrast to the hosts' defensive blunder, which led to the winning goal, the away side's back five proved to be the bedrock of an outstanding win at the Allianz Arena.
Despite Bayern having a lot more of the ball, the Bavarians were punished for their failure to make it count in the 62nd minute. An innocuous long ball led to confusion between Jerome Boateng, who failed to head away, and Manuel Neuer, who missed his punch. Igor De Camargo profited from the incompetence to bravely head the ball home into the vacant net and stun the capacity crowd.
Bayern unsurprisingly dominated possession in the early stages but a Mario Gomez header into the arms of Marc-Andre ter Stegen aside, the team created few clear cut chances. Gladbach, for its part, was content to allow Bayern the ball, sitting deep with the holding midfielders Havard Nordtveit and Roman Neustadter as American Michael Bradley is still out of favor.
The host side continued to keep the ball without threatening too often before Toni Kroos unleashed a low shot from outside the box on 25 minutes, which ter Stegen clutched onto at the second attempt. A defensive mix-up two minutes later almost set up Thomas Muller but he was denied by a last-ditch tackle from Tony Jantschke.
An Arjen Robben shot over the bar was then swiftly followed by another effort from Kroos who fired a left-footed strike the wrong side of the post on 37 minutes. From nowhere, Juan Arango later forced new Bayern goalkeeper Manuel Neuer into a fine stop with his shot four minutes before the break.
The beginning of the second period saw a more open encounter and ter Stegen was called upon on 48 minutes to make an excellent save to parry Gomez's header away from goal. Last season's leading goalscorer in Germany was then denied by the post on 54 minutes having produced a terrific header from Robben's near-post corner.
Once Gladbach had taken the lead against the run of play, it had to brace for a Bayern onslaught. Young goalkeeper ter Stegen was on hand two minutes after the opening goal to make a fine save from Robben's low shot.
Bastian Schweinsteiger then became the next player to be foiled by ter Stegen before substitutes Franck Ribery and Nils Petersen linked up on 77 minutes once Nordtveit had given the ball away. However, the new signing from Energie Cottbus chose the wrong option and the chance disappeared.
Bayern will be under pressure to produce an improved display next week when it travels to Wolfsburg. Stuttgart is Gladbach's opponent in round two and coach Bruno Labbadia was in the stands keeping an eye on his team's next rival.