Two first-half headed goals from Yang Xu and Diego Tardelli, proved enough for Shandong to book their place in the ACL group stages, which commence on 23 February.
But the Chinese outfit were made to work for their win, after Yongpo Wang was given an early shower 21 minutes from time, for a second bookable offence.
During a frantic finale to the clash, Shandong withstood a penalty, which was missed by Marcelo Carrusca, and an 89th minute Sergio Cirio goal.
Although Adelaide enjoyed a late flurry of chances - ultimately it proved too little, too late.
While the Reds started with promise and should have taken the lead after a goal-scramble in the 14th minute, which fell to defender Dylan McGowan, they were punished by Shandong just three minutes later.
Argentine Walter Montillo took full advantage after his compatriot Carrusca sloppily lost possession, and the resulting shot was parried by United goalkeeper Eugene Galekovic, before being headed home into an open goal by Yang Xu.
After taking the lead, Shandong, who finished last season in third place in the Chinese Super League, added a second goal in the 39th minute.
Montillo was again involved and cleverly found Yongpo Wang with a through ball, and the China midfielder in turn crossed the ball for Brazilian Tardelli, who made no mistake with his header.
But the Chinese side, who many believed would be short of a gallop, after their domestic season finished at the end of October, were put under immense pressure during an entertaining second-stanza.
The Reds, unbeaten in their last 10 A-League matches, found it hard to break their opponent's defence down for the most part, but two golden chances fell to midfielder Craig Goodwin.
Unfortunately for Adelaide, Goodwin couldn't finish off a sublime Carrusca cross in the 60th minute, as the 24 year-old misdirected his header wide of goal.
After Shandong were reduced to 10 men, Goodwin had a chance to make amends for his earlier miss, but his thunderous shot on goal was well saved by goalkeeper Dalei Wang.
Adelaide refused to go down easy though, and were presented with a lifeline after Mingjian Zhao was adjudged to have handled a Tarek Elrich cross in the 82nd minute.
But the usually reliable Carrusca, smashed his penalty into the crossbar, much to the disbelief of the home fans.
Cirio's late headed goal gave the hosts a glimmer of hope and although the Reds had numerous chances to restore parity during almost eight minutes of injury-time, Shandong hung on.
Adelaide have a chance to put their ACL disappointment aside in Sunday's away clash against Central Coast Mariners.
A win could see United, currently in sixth on the A-League table, move to as high as third.
Adelaide United 1 (Cirio 89')
Shandong Luneng 2 (Yang Xu 14', Tardelli 39')
Coopers Stadium, Adelaide
Referee: Minoru Tojo