The Montenegro striker opened the scoring in the fourth minute and his second goal, a minute after half-time, paved the way for a comfortable second period.
Mauricio Molina made it 3-0 and Damjanovic completed his treble seven minutes from time. Park Se-jik scored Jeonbuk's goal with a minute remaining.
The win takes fourth-placed Seoul eight points clear of Suwon Bluewings, who are the only team who can catch them but have only three games in which to do so.
Jeonbuk are a point ahead of their opponents in third, while the title race is between Ulsan Hyundai and Pohan Steelers.