Ha Seok-ju's men fell behind in the 11th minute thanks to Han Gyo-won's strike, but were level nine minutes before the interval courtesy of Macedonia international Stevica Ristic.
It looked as though both sides would have to settle for a draw, until Jeon Hyeon-chul struck a dramatic winner for the hosts in the third minute of stoppage time.
The result represented a second successive defeat for Jeonbuk, who had gone down to a similarly late winner at home to Seoul the previous week.
Pohang Steelers took advantage of Jeonbuk's loss to move level at the top of the table on 44 points with a 2-1 win at Ulsan.
The visitors had to come from behind, after Kim Shin-wook had put the home side ahead in the 27th minute.
Pohang levelled just two minutes later through Kang Soo-il, and a goal from Kim Jae-sung four minutes after half-time sealed all three points for Pohang, who overcame the disappointment of crashing out of the AFC Champions League on penalties to Seoul.
Seoul coach Choi Yong-soo had promised a more aggressive approach following goalless draws in both legs against Pohang, but witnessed yet another stalemate on Sunday as his side drew 0-0 with Jeju United.
Busan I'Park dropped to the foot of the table after being soundly beaten 3-0 at Incheon United.
Brazilian midfielder Ivo netted twice in the first half, before Kim Do-hyuk rounded off the scoring 17 minutes from time.
Busan replaced Gyeongnam at the foot of the table on goal difference, after Lee Cha-man's side went down 1-0 at home to Suwon Bluewings, with Roger netting the winner in the 81st minute.
Elsewhere, Park Jin-po cancelled out Lee Keun-ho's opener as Seongnam earned a 1-1 draw at Sangju Sangmu.
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