Rafinha's 55th-minute winner coupled with Pohang Steelers' 2-2 draw against Suwon Bluewings ensured Ulsan moved to the top of the Champions Group standings on goal difference.
Pohang looked set to retain their lead after they held onto the advantage supplied by Ko Mu-yeol's first-minute strike until the 75th minute.
Jong Tae-se found the equaliser and then fired Suwon ahead on 85 minutes to apparently give the visitors' fading title bid a major boost.
But Park Sung-ho popped up with an injury-time winner to rescue a point for Ulsan.
In the Relegation Group, Gangwon FC picked up an important 2-1 win over Gyeongnam.
Kim Bong-jin (26) and Kim Dae-kyung (34) sent the hosts 2-0 ahead before Yoon Suk-young (67) replied.
Joao Paulo grabbed an 82nd-minute equaliser as Daejon Citizen grabbed a 1-1 draw at Daegu FC. Derek Asamoah had scored Daegu's opener on 29 minutes.