In their final Group E game, Jiangsu's Asian-record signing Teixeira cancelled out Leonardo's opener, and ex-Manchester City striker Jo made it 2-1 to the visitors after half-time.
But Lim Jong-Eun equalised coolly for Jeonbuk on 68 minutes and it proved vital for the 2006 Asian champions from South Korea, who grabbed the point they needed to reach the last 16.
It was heartbreak for Dan Petrescu's Jiangsu, who splurged 50 million euros ($57.5 million) on Teixeira and also splashed out on Jo and Chelsea's Ramires in their bid for glory.
They join reigning champions Guangzhou Evergrande in departing what has been a mixed campaign for Chinese teams, despite a world-leading spending spree on players earlier this year.
However, Shandong Luneng will fly the Chinese flag alongside Sven-Goran Eriksson's Shanghai SIPG in the last 16 after they rounded off Group F with a 0-0 draw against Buriram United.
FC Tokyo pipped Jiangsu to second spot in Group E and go through with Jeonbuk after Ryoichi Maeda scored twice to hand them a 2-1 win over Vietnam's Binh Duong.
After a quiet start in Jeonju, Leonardo drilled Jeonbuk ahead from the penalty spot in the 19th minute after Choi Chul-Soon was clumsily fouled by Yang Xiaotian.
But Teixeira equalised for Jiangsu just five minutes later when he volleyed a ricocheting free-kick into the roof of the Jeonbuk net.
After a foul on Ramires, Jo converted the game's second penalty nine minutes after half-time to make it 2-1 to Jiangsu, but Jeonbuk were level again in the 68th minute.
In a well-worked corner move, a flick-on found Lim lurking at the back post and he neatly cushion-volleyed what transpired as a vital goal for Jeonbuk in front of their home fans.
Elsewhere Adriano struck his 10th goal of the competition as FC Seoul lost 2-1 away to Sanfrecce Hiroshima for their only defeat of Group F, but still finished top regardless.