The two sides began the day on 44 points, with the onus on Jeonnam to overhaul Ulsan in sixth - the latter holding the better goal difference.
And at one stage in their synonymous fixtures, Jeonnam were set to advance as they were level 1-1 away at Incheon United while Ulsan trailed 3-1 at Seongnam.
But Ulsan stormed home to win 4-3 with three late goals, rendering Jeonnam's own fightback from 3-1 down to draw 3-3 as consolation.
Tarta, Ho Lee and Park Dong-Hyuk all scored for Ulsan in a frantic finish, while Australian defender Robbie Cornthwaite scored two late goals to earn Jeonnam a point.
Ulsan's win keeps alive their hopes of breaking into the top-three and securing an AFC Champions League place, with five league matches in the championship round remaining.
Pohang Steelers, in the final Champions League spot in third, enjoyed a 3-0 win at home to cellar-dwellers Sangju Sangmu.
Runaway leaders Jeonbuk Motors were 1-0 winners at home to second-placed Suwon Bluewings, for their fifth straight league win and also taking them to a 10-match unbeaten streak in the top flight.
The result saw Jeonbuk move 10 points clear top of the table.
Gyeongnam edged Jeju United 1-0, while Seoul were held at home to Busan I'Park 1-1.
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