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.
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.
