The Japanese became the last side to seal a spot in the quarter-finals, yet they did it the hard way, losing 2-1 on a sweltering and nervy night in Shanghai.
Vitor Pereira's Shanghai join Chinese Super League (CSL) champions Guangzhou Evergrande in tumbling out of the competition at the last-16 stage.
Hulk, the 55.8 million-euro ($66 million) forward who missed the 3-1 first-leg defeat in Japan, returned to captain the hosts and needed just seven minutes to make his mark.
Shoma Doi levelled for Kashima before Hulk scored a penalty with nine minutes left to set up a dramatic finale.
But Shanghai were unable to find the goal to force extra time and Hulk said: "I feel full of pity because we had the dream of the Asian title, but now it is over.
"This is football, we fought to the end and now is the time to keep our heads up and focus on Sunday (against Jiangsu Suning in the CSL) and find three points."
The striker put his side on the way when he spun sharply in the box to fire into the net, sliding on his knees and pumping his fists in celebration.
Last year's semi-finalists had more of the ball but Kashima were a threat on the break and Mu Kanazaki might have equalised with their first chance, on 19 minutes, but his header flashed wide.
Shanghai, who top the CSL on goal difference but have stumbled of late under their Portuguese coach, did not heed the warning.
And Kashima made them pay three minutes before half-time when Doi adroitly steered the ball in to silence the home crowd.
Shanghai, for whom 60-million-euro Brazilian Oscar was largely anonymous until late on, went for broke in the second half.
Visiting goalkeeper Kwoun Sun-tae stood firm until Kashima conceded a penalty with 10 minutes left and Hulk just about beat Kwoun from the spot to set up a grandstand finish.
At one point in the second half, the benches of the two sides clashed, with players from both teams getting involved on the touchline.
Pereira played down the fracas, saying: "A football match is different from opera, in which we are quiet.
"Football is emotional and we want to win."
Kashima coach Go Oiwa insisted that he was never worried, even as Hulk and his teammates pushed for a third goal.
"I knew by looking at the players' eyes and faces that they were very strong mentally and we knew we could defend through the last 10 minutes. I was very confident they would do the job," he said.
Suwon Samsung Bluewings meanwhile beat fellow South Koreans Ulsan Hyundai 3-0 at home to progress 3-1 on aggregate.
The quarter-finals take place in August and September.