After Jeonbuk had dominated the first leg 4-1, Brazilian marksman Adriano gave the home side hope when he slotted a record-equalling 13th goal of the tournament in the first half.
But Jeonbuk's Ricardo Lopes doused any hopes of a comeback by equalising on 59 minutes, before Seoul's Ko Kwang-Min grabbed a consolation goal for Seoul in injury time.
Jeonbuk, the 2006 champions, now go into a blockbuster two-legged final next month against fellow former winners Al Ain and their feted playmaker Omar Abdulrahman.
The K-League leaders also reach their third Asian final despite a domestic scandal. They were deducted nine points and fined after one of their scouts was convicted of bribing referees.
FC Seoul's Adriano was in the thick of it during an electric first half in front of a noisy crowd as the hosts pressed for the goals they needed to overturn their first-leg deficit.
The Brazilian shot just wide on 16 minutes and headed off-target eight minutes later. Elsewhere, Jeonbuk midfielder Kim Bo-Kyung was bloodied by a flailing elbow before playing on with a bandaged head.
It was Adriano who lifted the home side's hopes when he charged on to Kim Chi-Woo's cutback to put Seoul 1-0 up on 38 minutes with his 13th goal, equalling the 2013 record of Guangzhou Evergrande's Muriqui.
A shock comeback was on the cards and FC Seoul came close to a second goal from a breakaway seven minutes into the second half, but ex-Arsenal forward Park Chu-Young's shot deflected wide.
And Seoul regretted their miss when Lopes turned Kim Chi-Woo and fired across the face of goal to make it 1-1 on the night and open up a yawning 5-2 aggregate lead.
Veteran substitute Lee Dong-Gook twice went close for Jeonbuk before Ko gave home fans something to cheer with a fierce drive two minutes into injury time.
It sets up a home-and-away Asian final between two sides of similar pedigree after Al Ain, who ousted Qatar's El Jaish on Tuesday, won the inaugural edition in 2003 and were runners-up two years later.