Josip Drmic squandered a brilliant opportunity to make it 3-1 in stoppage time at the culmination of a rapid counter-attack, before Bayern's Kwasi Okyere Wriedt saw an effort blocked on the line as Gladbach held firm to secure the points.
It remains to be seen how long the 26-year-old will be out of action, with Bayern set to host Hannover 96 on Saturday.
Bayern Munich's winning start in the Bundesliga in Jupp Heynckes' fourth stint in charge came to an end as they slumped to a 2-1 defeat at in-form Borussia Monchengladbach.
DF Mats Hummels, 6 - Always a threat in Gladbach's box but Bayern had left themselves too much to do after a timid first half display. "We started well, we know when we play against Bayern we need to defend all together, and we did", the Belgian said.
"He (Rodriguez) didn't know what the score was at half-time, so I assume it was a concussion, but we have to wait for a proper diagnosis", said Heynckes.
He came on for the second period in place of James Rodriguez, who suffered a suspected concussion in a clash of heads with Kramer's replacement Tony Jantschke.
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DF Niklas Sule, 5 - Sluggish alongside Hummels in central defence, giving away the penalty for handball in the box - his first defeat in a Bayern shirt in 10 Bundesliga appearances since joining from Hoffenheim.
Against Schalke and RB Leipzig he played a couple of very good games and soon that will be the standard.
"I touched the ball with a finger, if that's a penalty then that's sad", Sule, who has impressed for Bayern since his move from Hoffenheim, told Sky.
Dortmund coach Peter Bosz is under increasing pressure as his fifth-placed side are now winless in their last six league games dating back to late September.
The Colombian international was reportedly fine after the game, although Jantschke was taken to hospital.
DF Marco Friedl, 6 - Cannot be faulted on his league debut as Bayern were already two goals down by the time he entered the fray.