Kim Yong-Tae scored the only goal at Sungui Arena Park in the 76th minute to keep his side five points clear of Pohang Steelers at the top.
Ulsan are now on a four-match unbeaten run as they close in on the title.
Pohang have now gone eight games without defeat in all competitions following their 3-1 away victory over Busan I'Park.
Jang Hack-Yong put Busan - winless in eight - ahead in the 22nd minute, but Kim Seung-Dae levelled two minutes later.
The visitors stepped up a gear after the break, goals from Kim Won-Il and Lee Myeong-Ju securing three points.
In Saturday's championship round clash, Seoul defeated Suwon Bluewings 2-1 to pick up their first win in six.
In the relegation round, struggling Daejeon Citizen claimed a 3-2 win over Daegu, meaning they have achieved back-to-back victories for the first time since October last year.
Cesar Arias opened the scoring for the hosts at Daejeon World Cup Stadium in the fourth minute, but Hwang Il-Soo's double gave Daegu a half-time advantage.
Hwang Ji-Woong equalised in the 68th minute, before a dramatic stoppage-time winner from Anderson Plata.
In Sunday's other tie, Seongnam retained top spot in the relegation round table with a 2-1 win over Gyeongnam.
Lee Seung-Ryul and Server Djeparov sent Ahn Ik-Soo's men into a 2-0 lead within six minutes.
Kim Hyung-Bum pulled one back for the visitors nine minutes from time, but to no avail.
Seongnam moved back above Jeju United, who recorded a 1-0 win at Chunnam Dragons on Saturday through Lee Jin-Ho’s 87th-minute strike.
