The draw extended Leverkusen's run to 24 league matches without defeat this term, although Jupp Heynckes' team may come to regret dropping two points at home to a struggling mid-table team who lost 5-1 at home to VfB Stuttgart one week ago.
Stuttgart striker Cacau continued his prolific scoring run with two more goals in a 2-1 win over Eintracht Frankfurt while bottom club Hertha Berlin moved closer to relegation after a 2-0 home defeat against Hoffenheim.
The previous record unbeaten run from the beginning of a Bundesliga season was set by Bayern in 1988/89 - when Heynckes was also coach.
Leverkusen's run is also the longest without defeat at any stage of a single Bundesliga season.
They nearly went ahead in the 13th minute when Sami Hyypia's header was brilliant saved by Cologne keeper Farid Mondragon and defender Manuel Friedrich blasted the loose ball over the bar.
Shortly afterwards Stefan Kiessling, the Bundesliga's top scorer, volleyed wide after being set up by Eren Derdiyok.
Sebastian Freis had Cologne's first real chance when he beat off two defenders only to shoot straight at Rene Adler just after the half hour.
Leverkusen's halftime substitute Renato Augusto forced Mondragon to make a difficult save from a narrow angle shortly after the break and, although he came close again in the 75th minute, the game petered out into a goalless draw.
PROLIFIC RUN
Stuttgart's Brazilian-born Cacau, included in Germany's squad for next week's friendly against Argentina, added to his four goals in last week's win at Cologne and his effort in the 1-1 Champions League draw at home to Barcelona on Tuesday.
Stuttgart climbed to eighth with 34 points from 24 games after winning for the seventh time in nine league matches since Christian Gross took over as coach in November.
The goals all came in the closing minutes of the first half, Benjamin Koehler putting Eintracht ahead in the 39th minute.
Cacau, left unmarked at a corner, headed the equaliser two minutes later and scored the winner on the stroke of halftime with a 20-metre shot on the turn from Aleksandr Hleb's pass.
Sixth-placed Werder Bremen (38 points) ended Mainz's unbeaten home record with a 2-1 win, Sebastian Proedl notching the winner just after half time against the 10-man hosts who had Florian Heller sent off after 14 minutes for a bad tackle.
Tim Borowski had put Werder ahead with a free-kick just after the half hour and Burkina Faso striker Aristide Bance levelled for Mainz in the 45th.
Hoffenheim's Demba Ba and Vedad Ibisevic were on target to add to Hertha's troubles.
Struggling Nuremberg, who ended Bayern's run of 13 straight wins with a 1-1 draw last week, held VfL Bochum to a goalless draw to stay in 16th place, the relegation playoff spot.
Freiburg stayed two points above them with a 1-1 draw at Borussia Moenchengladbach
