The solitary point keeps Chunnam in fifth place, a point behind Seoul in fourth and Jeju in third place respectively.
For the hosts it was two points dropped especially as Incheon saw Jang Hyok sent off for a wild challenge after 33 minutes.
Jang had missed Incheon's best chance earlier in the half when he was through on goalkeeper Lee Woon-jae, only to see his shot saved by the former Korea Republic international.
After the sending off, Chunnam piled on the pressure with Brazilian duo Indio and Wesley going close - although both were unable to get the all important goal.
Incheon coach Huh Jung-moo said: "If the conditions had been better then we could have played a good game with Chunnam.
"As it was, it wasn't the best game but we will keep trying to pick up points and reach the play-offs."