Kang Min-Soo opened the scoring for the leaders and, although Yeom Ki-Hun levelled in the 36th minute, Kim Sung-Hwan sent Suwon to their fifth consecutive defeat with his strike on the stroke of half-time.
Ulsan hold a five-point lead with two games remaining and will hope to seal the title before playing title rivals Pohang Steelers - who were not in action - on the final weekend.
Jeonbuk Motors maintained their place in third, ahead of defending champions Seoul, with a 2-0 victory over Incheon United.
After a goalless first half Jeonbuk sprang into life with two goals in 10 minutes either side of the hour mark to seal all three points.
Jung Hyuk netted the opening goal in the 54th minute, with Lee Dong-Gook doubling his side's advantage.
Seoul remain just a point behind Jeonbuk after extending their unbeaten run to four games with a 3-2 win over Busan I'Park.
Dejan Damjanovic and Ha Dae-Sung gave the hosts a 2-0 lead, but Busan narrowed the deficit to 2-1 with Han Ji-Ho's 48th minute strike.
Damjanovic's 80th-minute penalty – his 17th goal of the season – sealed victory for Seoul before Yang Dong-Hyun's late consolation.
The fight to avoid relegation from the top flight continues, with four points separating the bottom three.
With Daejeon Citizen not playing there was a chance for Daegu and Gangwon to send the bottom side down, yet neither were able to win.
Gangwon fell to a 1-0 defeat as Lim Jong-Eun sealed victory for Chunnam Dragons, while Daegu battled to a goalless draw with Seongnam.
The final game of the round saw Jeju United fall to a second consecutive defeat as Gyeongnam produced a spirited display to win 1-0.
