Midfielder Ko struck on 76 minutes to ensure the hosts claimed a share of the spoils in their final K.League clash before next week's Champions League last-four tie with Western Sydney Wanderers.
Seoul had Wednesday's fixture brought forward to give them extra time to prepare for their crucial continental match, but were laboured and second-bottom Gyeongnam went ahead on the hour mark.
Jin Kyung-Sun fired his first goal of the season past Kim Yong-dae to put the visitors on course for a shock victory.
However, Seoul - who went into the game on a 12-game unbeaten run - rallied.
Ko spared their blushes, and Choi Yong-Soo's men can now look forward to next Wednesday's Champions League tie.