Seoul let slip a lead to lose to Gangwon, while Sunday's other K League fixture saw Pohang Steelers triumph at home.
Gangwon rallied from a half-time deficit to open the new K League season with an impressive 3-1 win, while newly promoted Busan I'Park were beaten on Sunday.
Seoul finished third in the 2019 campaign and they took the lead at Gangwon, Park Dong-jin's deflected shot finding the net to put the visitors ahead at the break.
However, the hosts hit back in the second half, starting with substitute Kim Ji-hyun converting a cross to level. They then secured victory with two late goals, the first of them scored by Cho Jae-wan with a clever back-heeled finish.
Having created his side's second, Kim Seung-dae sealed the result less than a minute later, cutting inside onto his right foot to score with a low finish.
Meanwhile, Pohang Steelers were too strong for Busan I'Park, running out 2-0 winners.
Stanislav Iljutcenko opened the scoring midway through the first half but the home team were made to wait to seal the points, Serbia midfielder Aleksandar Palocevic eventually doubling their lead from the penalty spot in the 71st minute.
The K League season finally began on Friday - Jeonbuk Motors recording a 1-0 triumph over Suwon Bluewings - following a delay due to the coronavirus health crisis.