The five-time winners took the first-half lead after Paulinho received a long pass from Philippe Coutinho down the centre of the field and chipped it over the outstretched arms of goalkeeper Vladimir Stojkovic.
After dominating possession, Brazil extended their lead through Silva who weaved his way through a pack of Serbian defenders before heading home a corner kick from Neymar and beyond Stojkovic in the 68th minute.
The 2-0 win secured Brazil place as group leaders while Switzerland, who drew 2-2 with Costa Rica, finished second and will also progress to the last 16 of the tournament.
