Having lost 1-0 to Al Hilal and then drawn 0-0 with German second-tier club Dynamo Dresden, City broke their pre-season duck thanks to goals in either half from Argentina international Sergio Aguero and Belgian captain Vincent Kompany.
City coach Roberto Mancini had to do without Italian striker Mario Balotelli and Spain midfielder David Silva, who were both granted three weeks’ holiday after featuring in the final of Euro 2012 in Poland and Ukraine.
Meanwhile, Bayern Munich fell 3-2 to Napoli in the final match of the Bavarians’ pre-season training camp on the banks of Lake Garda in Italy on Friday.
Napoli succeeded where they had twice failed in last season’s Champions League group phase, having been held to a 1-1 draw at home before losing 3-2 in the return match in Munich.
Young Austrian David Alaba opened the scoring for beaten Champions League finalists Bayern in the 17th minute, with Paolo Cannavaro equalising shortly before half-time.
New signing Xherdan Shaqiri equalised for Bayern after Macedonian striker Goran Pandev had put Napoli 2-1 up, only for 21-year-old forward Lorenzo Insigne to claim the winner for the Italians with seven minutes remaining.
Bayern were missing their eight Germany internationals, who are still on holiday after Euro 2012, as well as France winger Franck Ribery, who has resumed pre-season training on his own in Munich.
Jupp Heynckes’ side will fly to China on Sunday for two friendly matches: against Beijing Guoan in Beijing on July 24 and then Wolfsburg in Canton on July 26.