Shanghai overturned the first leg deficit with three second half goals from Kim Shin-wook, Stephan El Shaarawy and Alexander N'Doumbou.
After a goalless firat half, Kim - who joined Shanghai last July - was influential in the second period with the Korea Republic international firing home a half-volley to break the deadlock on the hour mark.
Shandong began pushing Shanghai back, but the hosts were not to be denied a second goal with El Shaarawy surging down the pitch and making it 2-1 on aggregate in the 81st minute.
The Cup was won two minutes later when N'Doumbou scored a screamer from outside the box, sending the home crowd into a frenzy.
Shanghai not only bagged their fifth Cup, but also a place in the 2020 AFC Champions League group stage.
The 2020 AFC Champions League official draw ceremony will take place at AFC House in Kuala Lumpur, Malaysia on Tuessay.