Silva, who will leave the Club at the end of this season, opened the scoring with a superb 20-yard free-kick, before slicing open the Cherries’ defence to set Gabriel Jesus up for our second.
Former City Academy player David Brooks provided a late scare when he pulled a goal back in the closing stages, but the home side held on under pressure.
The victory maintains City’s 100% record over Bournemouth in the Premier League, but Guardiola’s men were made to work hard for the three points against the relegation strugglers.
VAR showed Josh King to be marginally offside when he tapped in, whilst Ederson was at full stretch to superbly claw Junior Stanislas’ free-kick onto the post.
CITY+ subscribers can watch the full game in the video above.