Brazilian striker Obina broke the deadlock in the 34th minute and Lebanon midfielder Antar doubled his team's advantage eight minutes after the break with a header.
The visitors looked more dangerous from the outset but were unable to find the target while, at the other end, Obina volleyed past goalkeeper Wang Dalei only to see it ruled out for a foul in the build-up.
But the Brazilian then broke the deadlock when he steered Wang Yong-po's pass home from 10 yards.
Shortly after the interval, Hao Junmin delivered a measured cross for Antar to head past Wang and extend the hosts' lead.
"We were determined to play good football in the first half since we have often struggled in the opening 45 minutes in the previous matches," said Shandong manager Rajko Magic.
"Fortunately, my players overcame difficulties and they fully adhered to my original plan."
The win moved the defending champions onto 33 points, 12 adrift of leaders Guangzhou Evergrande.
"We tried to create trouble for our opponents but failed to grasp the early chances," said Shanghai coach Drazen Besek.
"We are looking forward to the next game and we will go all out for a victory."
Cameroonian midfielder Modeste M'bami netted a brace and Colombian striker Yovanny Arrechea added a third to give Changchun Yatai a convincing 3-0 triumph over Shaanxi Baorong at Changchun Jingkai Stadium.
Elsewhere, Beijing Guoan beat Nanchang Bayi 1-0, Dalian Shide edged out Qingdao Zhongneng 3-2 thanks to Martin Kamburov's last-minute winner and Chengdu Blades played out a 1-1 draw with Tianjin Teda.
Finally, Henan Jianye and Jiangsu Shuntian played out a goalless draw, as did Shenzhen Kingway and Hangzhou Greentown.