The draw was only the second time the hosts have failed to win in their last 35 matches across all competitions.
Four days after Germany’s stunning 6-0 loss to Spain, there was little in terms of redemption for Bayern’s many internationals, with the German champions failing to hit a single shot on target in the entire first half.
Werder took a deserved lead on the stroke of halftime after USMNT international Josh Sargent set up Max Eggestein who beat keeper Manuel Neuer with a well-placed left-footed effort. The German shot stopper also made his 400th appearance in a Bayern shirt.
Bayern, who had won 33 of their previous 34 games in all competitions, had to wait until the 50th minute for Douglas Costa to rattle the crossbar with a fierce shot and the hosts to show some signs of life.
They upped the pace briefly and Kingsley Coman drew them level, nodding in at the far post in the 62nd but for the next 20 minutes they again dropped back before a couple of late chances for Eric Choupo-Moting and Robert Lewandowski.
The hosts, however, have Neuer to thank for avoiding the second league defeat of their season after he beat Sargent in a one-on-one in the 88th minute.
Schalke 04 slumped to a 2-0 defeat at home against VfL Wolfsburg and have now gone 24 league matches without a win. Schalke, who are edging closer to the all-time winless run of 31 matches in the league set by Tasmania Berlin in 1965/66, are 17th.