First-half goals from Dejan Damjanovic and Mauricio Molina were enough for the visitors to seal the three points despite Lee Han-saem's second-half strike for Gwangju.
The win nudges Seoul two points ahead of Suwon Bluewings, who will return to the summit if they beat Ulsan Hyundai on Sunday.
Jeju United finished the day in third, a point behind Suwon, after they were beaten 1-0 away to Chunnam Dragons. Son Seol-min scored the only goal after 16 minutes.
The day's other games were drawn, with Daegu's Song Je-heon cancelling out Kim Hyeung-bum's opener to earn a point against Daejeon Citizen while Incheon United and Busan I'park shared a scoreless stalemate.