Pep Guardiola's team lacked the sharpness up front that they showed in the 7-1 demolition of AS Roma in the Champions League in midweek but the point gained puts the leaders on 21 points aheda of surprise package Gladbach in second.
Gladbach have now gone 14 games without defeat in all competitions this season.
Bayern had in-form winger Arjen Robben out injured and Franck Ribery on the bench but still looked dangerous and got their first clear chance after 10 minutes when David Alaba's curled shot was palmed onto the post by Yann Sommer.
The visiting Bavarians were in control in the first half but the home side had striker Robert Lewandowski under constant guard leaving last season's top scorer little space to move.
Gladbach forwards Max Kruse and Andre Hahn were denied by keeper Manuel Neuer as the hosts improved in the second half to confirm their status among the toughest teams to beat this term.
In stoppage time it was Sommer's turn to protect a point when he kept out a charging Claudio Pizarro from point-blank range.Neuer had to came to the rescue twice more, showing superb reflexes to tip Raffael's free kick wide at full stretch in the 67th and stopping the Brazilian's low drive 10 minutes later.