The German champions, chasing a record-extending 11th league crown, had possession but were far less effective than their opponents who looked to be snatching the three points courtesy of Ellyes Skhiri‘s fourth minute volley at the far post.
But Kimmich scored with a long-range effort to lift leaders Bayern to 36 points.
Buoyed by last week’s 7-1 demolition of Werder Bremen, Cologne were sharper throughout the first half and a step faster to the ball, keeping Bayern, who face Paris St Germain in the Champions League last 16 next month, well away from their box.
The Bavarians completely dominated after the break but despite the one-sided traffic could not find a way to score for much of the second half.
Substitute Thomas Mueller had their best chance but Marvin Schwaebe tipped his 80th-minute header over the bar. The keeper was beaten, however, when Kimmich’s missile went in off the bar in the last minute.