Cologne, who secured their top-flight status last weekend, were forced to play just over half-an-hour with 10 men after Matthias Lehmann picked up a second yellow card.
Augsburg tried to find a winner, although substitute Raul Bobadilla did go close with a direct free-kick before Alfred Finnbogason wasted two good chances.
It was too little for three points, but the draw takes the Bavarian side to within three points of safety with two games of the season remaining.
