The home side went ahead in the fifth minute thanks to Patrick Herrmann's cross, which caught Hans-Jorg Butt out and flew straight in, but Mario Gomez levelled in the 11th minute and Bayern dominated the game, going ahead through Bastian Schweinsteiger five minutes before the break.
Schweinsteiger missed a penalty before half-time and Gladbach took advantage of their second chance with goals from Marco Reus and Igor de Camargo putting them ahead.
But Philipp Lahm grabbed a point for Bayern in the 84th minute.
Gladbach made a flying start with Herrmann putting them ahead with only five minutes on the clock with a cross from the left which sailed beyond Butt into the Bayern net.
It was something of a false dawn for the home side as Bayern levelled little over five minutes later with Gomez continuing his excellent form with his eighth goal in five games.
He headed in powerfully after meeting a cross from Toni Kroos.
Bayern started to dominate affairs with Schweinsteiger heading against the underside of the crossbar after half an hour and Kroos then hitting the crossbar five minutes later.
The visitors took a deserved lead five minutes before the break when Schweinsteiger beat Christofer Heimeroth with a cheeky flick from Danijel Pranjic's low cross.
Bayern had the chance to wrap up the game moments later when Hamit Altintop was fouled inside the area by Sebastian Schachten, but Schweinsteiger's penalty hit the post.
Gladbach could and perhaps should have been out of the game, but they managed to turn the game on its head in the second half.
They levelled in the 56th minute with a quick counter-attack culminating in substitute De Camargo slipping the ball through to Reus, who made no mistake.
And another quick break four minutes later saw them go ahead, with Reus this time setting up De Camargo to shoot low into the far corner past Butt.
Bayern had to respond and they spent the last 20 minutes attacking the home side's goal.
Their equaliser was somewhat fortunate, however, with Anatoliy Tymoschuk's pass deflecting kindly into the path of Lahm, who picked his spot in the top corner of Heimeroth's goal to salvage a point for the defending champions.