Lee Dong-Gyeong struck in the 19th minute against the Harry Kewell-coached J.League outfit, who are appearing in the semi-finals of the continental championship for the first time, and the teams will meet again in Yokohama next Wednesday.
The result means Ulsan have booked a spot at next year's Club World Cup as one of Asia's representatives due to their ranking points.
Marinos defender Shinnosuke Hatanaka went close to opening the scoring in the 12th minute when he steered wide of the Ulsan goal while Marinos goalkeeper William Popp denied Um Won-Sang from close range moments later.
However, Ulsan took the lead when Lee slid the ball low to Popp's right from just inside the penalty area after Joo Min-Kyu's deft layoff.
Jo Hyeon-Woo saved from Yan Matheus in the 26th minute to maintain Ulsan's advantage and Jun Amano's effort soon after the restart was deflected wide for a corner as the visitors increased the pressure.
Ulsan then hit the post twice in the space of a minute, Joo striking the woodwork with a low left-foot strike before Lee saw his on-target attempt pushed onto the frame of the goal by the diving Popp.
Matheus thumped Amano's teasing cross over the bar from two yards out with less than 10 minutes remaining to leave Marinos behind at the halfway point in the tie.
Later on Wednesday, Saudi Arabia's Al Hilal, the four-time champions, were beaten 4-2 by hosts Al Ain from the United Arab Emirates in the Western Asian semi-final first leg.
Soufiane Rahimi's first half hat-trick put the Hernan Crespo-coached side on the cusp of a spot in the final as the Riyadh-based outfit's record-breaking run of 34 consecutive wins came to an end.
That match had been scheduled to be played on Tuesday but was postponed for 24 hours due to adverse weather conditions in the UAE.
The winners of the two semi-finals will face off over two legs in the decider next month, with the opening fixture in East Asia on May 11th and the return in the West two weeks later.
