Cologne picked up their first point in six games by containing hosts Hannover, who dominated possession but could not break the deadlock.
Japan forward Yuya Osako and defender Lukas Kluenter had chances for Cologne while Niklas Fuellkrug missed a good opportunity at the other end for Hannover.
The result means Hannover stay fourth in the table, missing the chance to climb above Bayern, who threw away a two-goal lead in Friday's 2-2 draw in Munich against Wolfsburg.
Borussia Dortmund are two points clear at the top after their 6-1 trouncing of Borussia Moenchengladbach on Saturday when Pierre-Emerick Aubameyang scored a hat-trick.
The pressure is growing on Cologne coach Peter Stoeger, who steered them to promotion from the second division in 2013-14 to finish fifth last season.
His team has now scored just one goal and taken one point in their first six league games.
"We got a point and we're happy with that," said Cologne defender Frederik Sorensen.
"We need to start scoring goals, though -- we can't survive without them.
"But we're fighting every game, and we'll see how far we get."