The diminutive Argentine playmaker produced a brilliant lofted through ball for Swedish striker Tobias Hysen to make it 2-0 in the 16th minute after new signing Yu Hai had opened the scoring.
Icelandic striker Vidar Orn Kjartansson sneaked in behind a sleeping backline to pull one back for the visitors six minutes before the break but the revamped and rebranded Shanghai were not to be denied the opening three points.
With the talented Conca, who enjoyed three trophy-laden years with Guangzhou Evergrande before leaving for Fluminense last year, and former England manager Eriksson at the helm, Shanghai are expected to provide a strong title challenge.
Evergrande lost Marcello Lippi as head coach in the close season but replaced him with another Italian World Cup winner in Fabio Cannavaro and are favourites for a fifth successive Chinese Super League crown.
The champions kick off their campaign on Monday at home to promoted Shijiazhuang Yongchang FC.
Last season's runners-up Beijing Guoan, the other fancied title challengers, also face promoted in Chongqing Lifan on Sunday.