Fernandinho was given a starting berth at Loftus Versfeld and the tourists looked strong in the first half, but could not find the breakthrough.
Pellegrini changed the entire XI at half-time, and the hosts needed only 11 minutes after the restart to break the deadlock.
Senegalese striker Mame Niang rose highest to nod the opener past Costel Pantilimon in the 56th minute, with a neat finish from South African forward Kermit Erasmus sealing matters nine minutes from time.
There were further disappointment to come for the Barclays Premier League runners-up, when Ivory Coast midfielder Yaya Toure limped off in the 83rd minute.
City continue their pre-season programme with a game against AmaZulu in Durban on Thursday night.