With only three outfield players on the bench, injury-hit Bayern looked on their way to victory when they recovered from a goal down to lead at halftime 2-1 thanks a Mario Gomez goal and a Bastian Schweinsteiger penalty.
With a stunning 79 percent possession in the first half, Bayern could have added more goals as they seek to climb up the table after a bad start.
But with just 16 points from 11 matches, they are down in ninth, trailing leaders Borussia Dortmund, who visit Hanover 96 on Sunday, by nine points. Mainz 05 lost a chance to go top for 24 hours at least when they were beaten 1-0 at Freiburg.
"We gave away a certain win in just 10 minutes in the second half," said Bayern coach Louis van Gaal.
"We have never played as good this season as in the first half but we just did not score enough goals. A top team is not allowed to lose the grip on a game in just 10 minutes," he told reporters.
Despite Franck Ribery, Arjen Robben and captain Mark van Bommel still out injured, Bayern, who advanced to the Champions League round of 16 in midweek with two games to spare, looked to have enough firepower against bottom-placed Borussia.
But in a frantic second half, Gladbach, transformed by the introduction of Brazil-born Belgian Igor de Camargo, outplayed the visitors, exposing their chronic defensive weaknesses.
Marco Reus combined well with the Belgian to level in the 56th minute and the roles were reversed four minute later as De Camargo fired them into the lead after Reus sent a pin-point through ball with defender Daniel van Buyten a step too late.
Lahm, who this week agreed to stay on at the champions until 2016, equalised with a well-taken chip from the right to take some pressure of Van Gaal, following his squabble with club boss Uli Hoeness over the team's performance.
Lacklustre Mainz 05 failed to take a provisional lead at the top slumping to defeat at Freiburg to remain in second place on 24 points.
Freiburg's top scorer Papiss Demba Cisse converted a 64th minute penalty to inflict Mainz's third defeat of the season. Niko Bungert had fouled Freiburg's Oliver Barth to concede the penalty.
Bundesliga top scorer Theofanis Gekas struck twice to take his tally to 11 and help third-placed Eintracht Frankfurt sink VfL Wolfsburg 3-1.
The Greek striker notched a goal in each half to keep Frankfurt's fine start to the season going and pile further pressure on Wolfsburg coach Steve McClaren, whose team remain in 12th place on 13 points.
Hamburg SV came from a goal down to beat Hoffenheim 2-1 with Croat Mladen Petric grabbing an 83rd minute winner that lifted his team to sixth place on 18 points.
On Friday, Schalke 04 got their first home win of the season when two goals from Raul and one from Klaas-Jan Huntelaar gave them a 3-0 win and lifted them to 15th place on nine points.
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