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.