Silva, also a scorer in the 3-0 win at Arsenal on Thursday, poked in David Silva’s cross at the back post just 35 seconds into the second half.
City dominated the game but had to be patient against a defensively-minded and unadventurous visitors.
Antonio Conte’s side did not have a shot on target in the match.
They have now lost four of their last five Premier League games and remain five points behind fourth-placed Tottenham.