- Simon Lorenz (59')
The visitors, who finished third in the second division, struck when substitute Simon Lorenz headed in the winner seconds after coming on in the 59th minute.
Cologne, who finished 16th in the Bundesliga, had several chances in the first half, including Ondrej Duda's low shot that whizzed wide of the post in stoppage time.
Yet after scoring Kiel went close to a second goal in the 78th minute but Janni Serra's header bounced off the crossbar.
Kiel, who survived late pressure to hold on for the win, host Cologne in the return leg on Saturday.