Kim Young-sam (three) and Han Sang-woon (68) scored the goals that kept alive Ulsan's hopes of topping the table at the end of the regular season.
Jeonbuk Motors, however, would have taken second place had they not been held to a 1-1 draw at fourth-placed FC Seoul.
Kevin Oris made the breakthrough in the 58th minute, but Dejan Damianovic earned the capital club a point by equalising four minutes later.
In fifth place are Incheon United, who beat Suwon Bluewings 3-0 thanks to goals from Lee Seok-hyun, Diogo Acosta and Han Kyo-won.
Seongnam Chunma are eager to climb into the top seven before the league splits and a 2-0 win over Gangwon FC saw them draw level with Busan I'Park.
Ivan Vukovic and Kim Dong-sub scored for Seongnam while Busan were beaten 2-1 at home by Jeju United. Kim Ik-hyun put Busan ahead, but a Luis Maranhao brace turned the game on its head.
Elsewhere, Daegu FC claimed a 3-1 win at bottom side Daejeon Citizen as Shim Dong-woon decided a 1-0 victory over Gyeongnam for Chunnam Dragons.