Second-placed Pohang, the reigning champions, looked set to suffer defeat after falling behind for a second time to a 79th-minute strike from substitute Kim Dong-chan at Steelyard Stadium.
However, Kang struck in the fifth minute of injury time to ensure the hosts remain two points behind leaders Jeonbuk at the top of the table.
Jeonbuk had claimed a first-half lead through Leonardo, only for Ryu Chang-hyun to reply in the 61st minute.
The draw between the top two represented good news for Suwon Bluewings, who now sit just three points from the summit after a 1-0 win at Sangju Sangmu on Saturday.
Brazilian forward Roger grabbed the only goal of the game midway through the first half, extending the Bluewings unbeaten run to seven matches.
At the other end of the table, rock-bottom Busan I'Park claimed a valuable 1-0 victory over Seongnam to join their opponents and Gyeongnam on 24 points.
Busan, whose only two wins in 24 previous league games had also come against Seongnam, emerged victorious courtesy of Fagner, who was on target shortly before the half-hour mark.
In the weekend's other matches, fourth-placed Jeju United suffered a surprise 2-0 defeat at home to Incheon United, while Jeonnam Dragons and Ulsan played out a 1-1 draw.
Jeonnam stay two points clear of Ulsan in the battle for a top-six finish and are now level with Seoul, who drew 1-1 with Gyeongnam on Wednesday.
