Jeonbuk began the game knowing that they had to score a goal or they would be knocked out.
Midway through the first-half Jeonbuk should have taken the lead when Kim Hyung-il's header landed at the feet of Lee Dong-gook but he blasted his shot wide from in front of goal, he should have scored.
The visitors nearly scored again in the 30th minute when Eninho's free-kick from 25-yards out went narrowly wide of Yang Zhi's right post.
The teams went in at half-time with the scores tied 0-0 with Jeonbuk looking the more likely to score.
In the 72nd minute Jeonbuk took the lead when midfielder Lee Jae-sung slipped a beautiful ball into Edu, who side-footed home from close to make the score 1-0.
The Brazilian then had two chances to kill the game off, first when his shot from close-range was well saved by Yang, and a volley from in front of goal hit the bar to go out of play.
In the 80th Beijing scored but the goal was disallowed when midfielder Ha Dae-sung was adjudged to have fouled goalkeeper Kwoun Sun-tae before scoring.
The visitors nearly got a second goal when Leonardo shot from 20-yards out was brilliantly saved by Yang in the 82nd minute.
Beijing's Zhou was then shown a straight red for a foul on defender Choi Chul-soon in injury time.
Pablo Batalla nearly got the equaliser at the death but his shot from the edge of the area was saved by Kwoun as the visitors held on for the win and a quarter-final berth.