Kevin Oris scored the only goal after 65 minutes as Daejeon notched only their sixth win of the season.
The result lifts them off the foot of the table while Jeonbuk hold a narrow one-point lead over FC Seoul at the top.
Ulsan Hyundai edged out Suwon Bluewings 3-2 to climb above their opponents into third place.
Yang Sang-Min fired Suwon in front after 19 minutes but the hosts responded with goals from Kwak Tae-Hwi (25) and Kim Shin-Wook (44).
Choi Jae-Soo levelled the scores after 51 minutes but Kim scored his second of the match 10 minutes later to secure the points for Ulsan.
In today's other fixture, Park Sung-Ho grabbed a brace and Noh Byung-Joon was also on target as Pohang Steelers beat Seongnam Chunma 3-1.
Seongnam had gone in front through Jael Ferreira.