The hosts emerged victorious from a match that pitted first against third on Wednesday as Jeonbuk stayed ahead of defending champions Pohang Steelers in the race for the Korean top-flight title.
Jeonbuk appeared to be heading for defeat after Yeom Ki-hun and Kim Do-heon gave Suwon a 2-1 lead in the 62nd minute following Lee Dong-gook's 23rd-minute opener.
However, two goals in the space of three minutes settled the game in Jeonbuk's favour, striker Lee taking his tally for the season to 12 with the winner after Han Gyo-won levelled matters.
Pohang remain a point behind in second, defender Shin Kwang-hoon scoring the only goal of the game to secure a 1-0 victory against Seongnam.
Jeju United and Jeonnam Dragons both missed the chance to leapfrog Suwon into the third as each suffered surprise defeats.
Fourth-place Jeju lost 3-2 at home to Sangju Sangmu, while Jeonnam were beaten 2-1 by Incheon United, who claimed their first away success of the season to pull two points clear of the foot of the table.
Midfielder Leandro Lima gave Jeonnam the advantage, only for Jin Sung-wook and Park Tae-min to turn things around for Incheon.
Kim Shin-wook's 59th-minute strike tightened Ulsan's grip on the sixth and final championship round spot, the attacker sealing a 1-0 triumph at Seoul to give his side a five-point lead over the seventh-placed capital club.
Elsewhere, bottom club Gyeongnam played out a 1-1 draw with fellow strugglers Busan I'Park.
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