The visitors actually led through Rafinha in the 36th minute, but were pegged back eight minutes later by Lee Myung-joo.
Nevertheless, Ulsan moved second in the league and remain only a point behind the leaders with a game in hand.
Suwon Bluewings and Incheon United also drew 1-1 in the day's other game in the championship group, Santos giving Suwon the lead before Ahn Jae-gon levelled.
In the relegation group, Daegu were cast adrift in the relegation play-off spot after a 3-0 defeat to nearest rivals Gyeongnam.
Jeong Shung-hoon and Lee Jae-an struck in the first quarter-hour and Kang Seung-jo's second-half goal clinched a win which lifts Gyeongnam five points clear of the bottom three.
Daejeon Citizen remain rock-bottom after a 2-2 draw with Chunnam Dragons.
Lee Dong-hyun and Jung Seok-min put Daejeon on course for a win which would have lifted them ahead of Gangwon, but Wesley netted a late equaliser for the Dragons, for whom Lee Jong-ho had opened the scoring.