Yan Dinghao put the seven-time champions ahead with 12 minutes on the clock before Wei doubled Guangzhou's lead with a stunning curling effort from almost 25 yards eight minutes before halftime.
Wei then put the result beyond doubt six minutes after the interval when he latched on to Huang Bowen's ball over the top of the Shanghai defence before slotting beyond Chen Zhao.
"I'm very satisfied with where we are in the standings," said Guangzhou head coach Fabio Cannavaro.
"So far we have only lost two games in the league and the young players have seized their opportunities and produced very good results."
Guangzhou's win moves Cannavaro's side up to second place, ahead of defending champions Shanghai SIPG on goal difference and just two points adrift of leaders Beijing.
Roger Schmidt's side suffered only their second defeat of the season on Sunday when they slipped to a 2-0 loss at the hands of Shandong Luneng, for whom Roger Guedes scored twice.
Beijing lead the standings with 39 points from 15 matches played in the 30-game season while SIPG also closed the gap to the leaders as a result of their 1-0 win over Shenzhen FC.
Former Chelsea star Oscar scored the only goal of the game four minutes after halftime to ensure Vitor Pereira's champions won for the 12th time this season.
Elsewhere, Dalian Yifang secured a much needed 3-1 victory over Beijing Renhe to move further from the relegation zone, with Yannick Carrasco and Marek Hamsik both on the scoresheet.
Jordi Cruyff's Chongqing Lifan defeated Tianjin Teda 1-0 to climb up to fifth and Guangzhou R&F overcame the absence of the league's leading scorer, Eran Zahavi, due to suspension to defeat Henan Jianye 2-0 thanks to a brace from Dia Saba.
Hebei CFFC's troubles continued with a 2-0 loss at the hands of Wuhan Zall that leaves them in 13th place - just two places and one point above the relegation zone.
Tianjin Tianhai, meanwhile, remain rooted to the bottom despite picking up a point with a 2-2 draw against Jiangsu Suning, the last-placed side's third draw in a row leaving them on just 10 points.
(Reporting by Michael Church, Editing by Alison Williams)
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