Xherdan Shaqiri salvaged a point for the league leaders with the equalizer in the 59th minute, canceling out Thorben Marx's well-struck 21st minute penalty.
Marx scored with Borussia's first shot on goal after Jerome Boateng was adjudged to have blocked Tolga Cigerci's cross with his arm.
"I don't think it was a penalty," said Boateng. You can give it," said Moenchengladbach coach Lucien Favre.
Bayern had 26 shots on goal compared to for the visitors' six, but struggled to create clear chances in the face of dogged defending and an impressive performance from Borussia goalkeeper Marc Andre ter Stegen.
"There was too much to do," Ter Stegen said.
The result leaves Bayern 12 points clear of Bayer Leverkusen ahead of the rest of the final games before the winter break.
Moenchengladbach moves provisionally sixth after its fifth game without defeat.
Bayern coach Jupp Heynckes, who remains Moenchengladbach's all-time top-scorer from his playing days, sent out the same 11 for the first time this season, and the home side made the better start with Franck Ribery looking dangerous in particular.
The Frenchman skipped past two defenders and played the ball in, only for Ter Stegen to snuff out the danger.
Bayern had penalty appeals of its own after Marx scored, but Thomas Mueller fell easily under Oscar Wendt's challenge.
Patrick Herrmann might have scored at the other end when Manuel Neuer — in his 50th Bundesliga game for Bayern — inexplicably emerged from goal, only for Dante to save his goalkeeper's blushes by cutting out his former teammate's weak effort on the unguarded net.
Javi Martinez, who overcame a cold to play, was forced off with a facial injury in the 38th, when Shaqiri came on in the Spaniard's place.
Ter Stegen produced an outstanding save to deny Bastian Schweinsteiger after the break, when the home side maintained its pressure but consistently failed at the final pass.
Shaqiri eventually capitalized on a Marx mistake before beating Ter Stegen at the near post for his first Bundesliga goal.
Gomez claimed a penalty two minutes later, though TV replays showed Roel Brouwers got a slight touch to the ball, and Moenchengladbach did enough to hold on.
"Ter Stegen was the outstanding man," Heynckes said. "We didn't know how to make it 2-1 from all the chances."