The hosts went ahead in the first half through Joshua Kimmich’s header but were denied all three points as the visitors levelled after the break to end their perfect start.
Bayern Munich dropped their first Bundesliga points of the season as Anthony Modeste’s second-half equaliser gave Koln a shock 1-1 draw at the Allianz Arena.
Carlo Ancelotti’s side had suffered defeat to Atletico Madrid in the Champions League last time out and failed to get back on track despite Joshua Kimmich heading his fifth goal of the season in the first half.
Koln came into the game sitting fourth after an impressive start to the campaign and Modesete scored in acrobatic fashion on 63 minutes shortly after Javi Martinez had hit the post for Bayern, who made seven changes after their midweek defeat.
Substitute Thomas Muller thought he had rescued the points for Bayern, but a brilliant save from Timo Horn, as well as Juan Bernat striking against the post, ensured the visitors claimed a point.
Bayern – who had scored four on each of Koln’s last two trips to Munich – stay top, but title rivals Borussia Dortmund can move to within one point if they defeat Bayer Leverkusen later on Saturday.
Arjen Robben was handed his first start of the season and made a lively start, firing just off-target with two efforts from outside the area.
Rafinha also threatened, driving a shot just over the crossbar, while Mats Hummels should have done better with a close-range header from Robben’s corner.
Koln ventured forward when Yuya Osako tested Manuel Neuer from distance in the match’s first shot on target and Robert Lewandowski could only fire a free-kick from 20 yards against the wall at the other end.
But just as it looked like Bayern would go into the half-time interval frustrated, the in-form Kimmich struck.
Bernat impressively evaded the challenge of Marcel Risse down the left and sent an inviting delivery that Kimmich converted with an accurate diving header from inside the six-yard box.
Thomas Muller replaced Robben for the second half, which started with Renato Sanches forcing Horn into a low stop.
Modeste had a penalty claim turned down as he was challenged by Mats Hummels in attempting to get on the end of Jonas Hector’s cross, while Osako headed wide in another chance for the visitors.
Bayern could have made sure of the result, only for Muller to fire wide and Lewandowski to head over in decent chances created by Bernat and Kingsley Coman respectively.
Ancelotti’s side went even closer when Martinez saw his header bounce off the foot of the post from Xabi Alonso’s corner.
Those misses became more significant when Modeste netted his fifth Bundesliga goal of the campaign, stretching impressively to prod in a clever right-footed finish that caught out Neuer as the striker got on the end of Riise’s right-wing cross.
Ancelotti brought on David Alaba and Arturo Vidal for Coman and Sanches in an attempt to find a late winner, but Bayern had their hearts in their mouths when Osako appeared to have scored, only to be flagged offside from Salih Ozcan’s throughball.
Muller thought he had fired Bayern to victory, but looked on in disbelief when Horn somehow got down to push his volley onto the woodwork.
Lewandowski – on his 200th Bundesliga appearance – saw a penalty claim denied after going down under Frederik Sorensen’s challenge, while Bernat sent a late drive against the post.
Amazingly, Koln could have won it when substitute Simon Zoller raced clear in stoppage-time to cap a fast counter-attack, but he missed the target when one-on-one with Neuer. Still, the visitors greeted the final whistle with joyous celebrations.