The defending champions have now won eight of their 10 league games so far this season and are threatening to run away with their fourth title in seven years.
With national coach Uli Stielike watching from the stands, Lee Dong-guk opened the scoring from the penalty spot in the 64th minute at Ulsan's Munsu Stadium but the Tigers equalised through midfielder Chikashi Masuda two minutes later.
Ulsan fans barely had time to celebrate when Jeonbuk went back in front through Edu in the 68th minute.
Ulsan got off to a strong start this season under new coach Yoon Jung-hwan but have faltered in recent weeks, and Sunday's loss means they have now gone six games without a league win.
Yoon was unable to take his place on the bench on Sunday after receiving a two-game ban for abusing the referee in their previous match against Jeju.
While Jeonbuk appear to be romping to another title, the demands of also competing in the Asian Champions League (ACL) are starting to take their toll.
"It was the players' mental strength that overcame the physical difficulties we had," Jeonbuk coach Choi Kang-hee told local media. "The players took a lot of confidence from this win and now we must prepare well for the ACL."
Jeonbuk play Chinese side Beijing Guoan in the last 16 of Asia's top club competition later this month.
National team coach Stielike marvelled at Jeonbuk's consistency but was a bit concerned that the league could turn into a procession.
"Jeonbuk are on such a roll right now, and if a team like Ulsan can't match them then I don't know who can," he said.
Suwon took advantage of slip-ups by their rivals in the top half of the table to climb to second spot with a 2-0 win at Gwangju.
Jeju went down 1-0 at Incheon, Pohang were held 2-2 at home by Seongnam and Jeonnam could manage only a 0-0 home draw with bottom club Daejeon.
FC Seoul claimed their third win of the season, a 1-0 victory over Busan, but are third from bottom. (Writing by Peter Rutherford; Additional reporting by Sohee Kim; Editing by Nick Mulvenney)