The result means Gamba secured a convincing 6-3 victory over their Korean rivals and puts the Japanese giants into the last eight of the tournament for the first time since their won it in 2008.
Brazilian forward Anderson Patric opened the scoring for the hosts at the at Expo '70 Stadium, before Shu Kurata added a second just before the half-time break.
Yun Ju-tae then scored twice for the visitors either side of Gamba's Brazilian substitute Lins' goal in the second half, but the Koreans were unable to find the additional three goals they required to advance.
After winning last week's first leg 3-1 in the Korean capital, Gamba quickly extended their advantage in the tie to three goals in the 16th minute when Patric was found unmarked in the Seoul box by Takashi Usami and the striker made no mistake with a headed finish.
Seoul were handed a reprieve just before the half-time break when they were awarded a penalty, but Colombian midfielder Molina dragged his spot-kick wide and the opportunity was gone.
Shortly afterwards, Gamba doubled their advantage on the night when Kurata claim the ball inside the Seoul box after a few scrappy exchanges and drilled his effort past Kim in the Seoul goal.
The hosts continued to dominate proceedings after the half-time break, but conceded a goal against the run of play four minutes before the hour when Shim Je-hyeok's low cross was steered in, via a deflection, by Yun.
The rest of the match produced few goal-scoring chances until the very end of the match when, with three minutes remaining, Lins made no mistake from Koki Yonekura's cross and headed home with a deft finish.
With the match as a contest largely over, Yun added his second of the night in stoppage time.