The first opportunity arrived for Darmstadt when a loose ball broke to Jan Rosenthal, whose powerful volley drifted just wide of the post.
Marcel Risse came agonisingly close to breaking the deadlock at the other end when he curled past the post, but it proved to be the first sign of the visitors taking control of the contest.
Despite spending most of the first half on the back foot, Darmstadt could have been ahead at the break had Sandro Wagner not miscued his effort wide after connecting with a cross.
It was the visitors who continued to dominate possession, but with chances difficult to come by in the second half, Darmstadt were keen to protect the point heading into the closing stages.
Koln settled for the draw which stretches their unbeaten run to four games, while Darmstadt are now five points clear of the bottom three.