New City coach Manuel Pellegrini returned after compassionate leave to see his charges record the first victory of his tenure, with the two matches on their tour to South Africa having both ended in defeats.
The Chilean included midfielder Fernandinho, one of the Blues' summer signings, in the starting line-up and saw his team look comfortable in the opening exchanges, with Dzeko firing into the side-netting and Yaya Toure then having a header saved.
On a difficult surface churned up by torrential rain and the first semi earlier on Wednesday, City produced a workmanlike performance with only man-of-the-match James Milner producing any real quality of note.
It was the tireless England midfielder who crossed from the right in the 21st minute for Dzeko to head down and in from close range. That proved to be the only goal of the game.
The next time City really looked threatening was two minutes after the break as Toure flashed an effort across the face of goal and wide.
The well-organised South China side then enjoyed a spell of pressure, before Toure was substituted for new recruit Alvaro Negredo, who was making his unofficial Blues debut. The Spaniard soon sent an acrobatic effort over the bar.
Dzeko came closest to a second goal when he powered a shot at the keeper from Negredo's ball into the box, as City set up a final clash against Sunderland on Saturday.