It could have been worse for the AFC Champions League quarter-finalists, who have yet to win in July after also being held to draws by FC Seoul and Ulsan, as they needed an own goal to earn a point.
Lee Sung-ki put Gwangju ahead in the 57th minute, slotting in the rebound after Park Dong-ki has seen his shot blocked, but Jeonbuk salvaged a draw with an equaliser soon after when Park Won-jae's cross bounced off Kim Su-beom into his own net.
"For us, a draw feels like a defeat," said Jeonbuk coach Choi Kang-hee. "This is the third game without a win. There is nothing especially wrong with how we are playing and with the mood in the camp but we need to take a look at things. We have a home game next week and will get ready for that."
Second-placed Pohang Steelers can cut the gap at the top to one point if they defeat FC Seoul on Sunday.
Jeju United stay in third after drawing 2-2 at Seongnam Ilhwa.
Jeju looked on course for a second successive defeat when they fell 2-0 down following strikes in quick succession from Brazilians Heverton and Everton Santos in the first half
However, two goals in the final 14 minutes from Park Hyun-beom saw Jeju hit back and claim a share of the spoils.
Busan I'Park go fourth, level on 29 points with Jeju, following a 2-1 win at Sangju Sangmu. Kim Cheol-ho put Sangju ahead but goals from Han Ji-ho and Park Tae-min gave Busan the win.
Suwon Bluewings edged closer to the play-off places with a 1-0 victory at home to Incheon United, new signing Stevica Ristic netting the winner just before the break with his second goal in successive games.
Elsewhere, Ulsan Horang-I won 2-1 at bottom club Gangwon FC with goals from Kim Shin-wook and Lee Jin-ho cancelling out an effort from Lee Jung-woon for the hosts, while Gyeongnam FC thrashed Daejeon Citizen 7-1.
Yoon Bit Garam, Lee Hyo-gyun, Lee Hoon, Park Min, Luke Devere, Jordan and Lucio got the goals for Gyeongnam while Lee Woon-hee got a late consolation for Daejeon.