Former Southampton and Italy forward Graziano Pelle was on target from the penalty spot just after the hour mark to put Shandong 2-1 up after Zheng Dalun had cancelled out Wu Xinghan's opener for last year's Chinese FA Cup runners-up.
Zhou Haibin and Zhang Chi put the result beyond doubt with goals in the 64th and 68th minutes respectively before Yang Xu netted a consolation for the home side in stoppage time.
"This was our first away game of the new season and all of the players did their best," coach Li Xiaopeng said. "We had luck on our side and scored some beautiful goals and that's thanks to the players."
Shandong move on to seven points from their first three games and are two points behind the leading trio of Shanghai SIPG, Beijing Guoan and Guangzhou Evergrande.
Defending champions SIPG had midfielder Odil Ahmedov to thank for their 2-1 win over Hebei CFFC, with the Uzbekistan international scoring the winner 10 minutes from the end.
Guangzhou Evergrande claimed all three points with a 1-0 win over Dalian Yifang courtesy of a late Anderson Talisca goal.
Yu Dabao scored the only goal of the game in the Beijing derby as Roger Schmidt's Guoan saw off Beijing Renhe to also move on to nine points from their first three fixtures.
Promoted Shenzhen FC's perfect start came to an end when Adrian Mierzejewski earned Chongqing Lifan a 1-0 win while last season's second division champions Wuhan Zall also lost with goals from Wang Song and Wu Xi securing Jiangsu Suning a 2-1 victory.
Gio Moreno's 88th-minute goal gave Quique Sanchez Flores his first win of the season as Shanghai Shenhua downed Henan Jianye 2-1, with the Colombian netting after Odion Ighalo had given Shenhua the lead seven minutes after the break.
Feng Zhuoyi looked to have earned Henan a point seven minutes from full-time when he netted from close range after a defensive mix-up, but Moreno volleyed home Fredy Guarin's lob into the area five minutes later to ensure Shanghai went home with all three points.
Frank Acheampong sealed Tianjin Teda's first win of the season as they edged out Guangzhou R&F 4-3 in a thriller, with the winner coming three minutes into injury time from the Ghana striker.
