Bayern Munich dropped points for the first time in the Bundesliga this season when Anthony Modeste's athletic finish gave Cologne a 1-1 draw at the champions on Saturday.
But rivals Borussia Dortmund failed to capitalize and lost for the second time this term when they were deservedly beaten 2-0 at Bayer Leverkusen in the late match.
Second-bottom Hamburg remain without a win from six games played after new coach Markus Gisdol's debut ended in 2-0 loss at second-placed Hertha Berlin while Ingolstadt's horror start also dragged on with a 2-1 home defeat by Hoffenheim.
Werder Bremen's revival under Alexander Nouri was checked by a 2-2 draw at fellow strugglers Darmstadt and Eintracht Frankfurt's good start to the season evaporated in a 1-0 defeat at promoted Freiburg.
Bayern coach Carlo Ancelotti made seven changes to the side which lost at Atletico Madrid in the Champions League in midweek with Arjen Robben enjoying his first league start in six months.
At first, the home team's prodding and probing was making little difference against a solid Cologne defence which has impressed this season.
Eventually the deadlock was broken and from an increasingly likely source. Joshua Kimmich is a midfielder by trade but spent much of last season as an emergency centre back.
Now he has turned himself into a goalscorer, netting his third of the league season when his diving header met Juan Bernat's cross five minutes before the break.
Kimmich has also scored for Germany and in the Champions League this campaign and is fast becoming one of the stars of the German game.
With Arnold Schwarzenegger in the stands, Bayern had hoped to terminate the match as a contest but Cologne levelled on 63 minutes when Modeste acrobatically turned in Marcel Risse's cross.
The French striker might have been better heading the ball, but instead leapt like a salmon to score his fifth league goal of the season with his foot.
Both sides could have won it with Timo Horn superbly denying Thomas Mueller and Bernat striking the woodwork before Simon Zoller really should have scored for fourth-placed Cologne but dragged his shot wide.
"Our players are becoming more experienced and hardened and are showing our quality," Cologne coach Peter Stoeger told a news conference.
"We are very happy. A point at Bayern doesn't happen every day."
Bayern's injury-prone winger Robben only managed 45 minutes before being withdrawn with a rib problem.
"He had pain and couldn't continue but it is nothing bad," Ancelotti said.
Bayern top the table with 16 points and Dortmund missed the chance to cut the gap to just one when they slipped up in Leverkusen.
Dortmund, in third on 12 points like Cologne, never really got going and were behind after 10 minutes when Admir Mehmedi headed in a corner after marker Julian Weigl slipped.
Sokratis Papastathopoulos then had a shout for a penalty turned down for the visitors and Pierre-Emerick Aubameyang missed a good chance.
But seventh-placed Leverkusen, inconsistent this term, would not be denied and Javier Hernandez sealed the win 10 minutes from time when he finished off Hakan Calhanoglu's cross.
Following the sacking of Bruno Labbadia last weekend, Hamburg failed to reward new coach Gisdol with any points after Vedad Ibisevic clinched a 2-0 home win for Hertha.
The forward poked in on the half hour after a scrappy passage of play and then converted a second-half spotkick to take the Berliners onto 13 points and leave Hamburg with just one from six games.
While Hamburg's performance was not as shocking as their pink away kit, they failed to impose themselves although returning forward Pierre-Michel Lasogga did hit the bar with a free kick.
Gisdol said: "Hertha are a very difficult side to play. They are sure of themselves and are an established outfit."
Bremen looked like they had come from behind to win for the second straight game under interim boss Nouri but Antonio Colak grabbed his second goal of the game to salvage a draw for Darmstadt in the 73rd minute.
Croatian Colak had bagged the opener, his first goal in the Bundesliga, from the penalty spot after Theodor Gebre Selassie fell back into Jerome Gondorf.
Fourth-bottom Bremen rallied thanks to Ludovic Sane and Serge Gnabry but the lead did not last.
Ingolstadt are a place below Bremen on just a point with second season syndrome appearing to kick in.
Hoffenheim's Sandro Wagner netted from close range at the far post following a quick counter-attack on 11 minutes. Another speedy first-half break led to Kerem Demirbay slamming home from outside the area for 2-0.
A late Lukas Hinterseer penalty was of little use to Ingolstadt.
Freiburg's Vincenzo Grifo scored with a well-placed finish in the fourth minute to down Frankfurt and move his side up to nine points, one below their opponents.
It was Freiburg's ninth home win in a row.
In Friday's game, promoted RB Leipzig added to their burgeoning reputation with a 2-1 home win over Augsburg and sit fifth.
On Sunday, bottom side Schalke go in search of their first points at home to Borussia Moenchengladbach while Wolfsburg host Mainz.