Despite Dominic Calvert-Lewin cancelling out Gabriel Jesus’ opener, goals from Riyad Mahrez and Raheem Sterling kept City in touch with league leaders Liverpool.
Silva, the former Spain international, replaced Sterling with four minutes remaining at Goodison Park to make his 289th appearance and collect his 200th top flight victory.
In doing so, the City captain became the fastest player to reach that accomplishment, managing it 16 games quicker than previous record holder, Chelsea legend John Terry, who won the same amount, but in 305 matches.