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.
Silva handed City the perfect start, expertly curling the ball beyond the helpless Aaron Ramsdale via the underside of the crossbar after Jefferson Lerma’s foul.
It looked as if it would be a long night for the visitors, but with City not at our slick best, Eddie Howe’s side rallied.
King fired wide under pressure, before Ederson's stunning save from Stanislas' set-piece and then Otamendi threw his body in the way to deflect Dominic Solanke’s close-range effort over the bar.
The visitors were left lamenting missed opportunities when Jesus latched onto Silva’s precise through ball, cut inside two defenders and fired expertly into the far corner.
It did little to reduce Bournemouth’s endeavours and they continued to attack with the conviction you’d expect from a team fighting for their Premier League lives.
Stanislas created two opportunities, the first was converted by King but ruled out by VAR for an incredibly tight offside, whilst the second saw Ilkay Gundogan block Dan Gosling’s half-volley after Ederson spilled a cross.
VAR was called into action again when Steve Cook brought down Jesus in the area.
Referee Lee Mason awarded a penalty, but replays showed it was the Brazilian who had stood on the Cherries’ captain’s foot.
Late in the game, Phil Foden danced between Jack Stacey and Cook but shot straight at Ramsdale and it meant City were forced to endure a nerve-jangling finale.
It started when Brooks guided Wilson's cross into the bottom corner and in six minutes of added time, Ederson's defence were forced to withstand a late onslaught, with the ‘keeper diving at the feet of Sam Surridge to maintain our lead.
Silva signing off in style
David Silva is bowing out at the top.
This was another classy display in which he was the architect of our attacking play.
Playing as the most advanced of the midfield trio, he proved elusive for his Bournemouth counterparts, adopting positions in the space between their defence and midfield and knitting everything together for Guardiola’s side.
His goal and assist were vintage Silva, a showcase of his standard-setting technique and awareness.
He is in fine form as he enters the part of the season which will determine whether he enjoys the perfect swansong he deserves.
pEP gUARDIOLA: a DIFFICULT GAME
"It was a really difficult game, they played really well. We could not control it. Their high pressing was good.
"They played with a need to stay in the Premier League. We played well in some moments. The same is going to happen against Watford. It will be so tight. It is normal."
Man of the match - David Silva
Who else? On a tough night for City, his quality was the difference.
Guardiola has won 111 of his first 150 Premier League games, six more than any other coach at this stage of their career in the competition.
What it means
With Chelsea unable to catch City, this win does nothing to alter the Premier League table. City are guaranteed second place, with 75 points after 36 games.
However, a third successive victory ensures Guardiola’s side go into the FA Cup semi-final against Arsenal in good form.
City face the Gunners at Wembley on Saturday 18 July, with kick-off at 19:45 (UK), when we will try to reach the FA Cup final for the second consecutive year.
SUBS: Carson, Laporte, De Bruyne, Doyle.
BOURNEMOUTH XI: Ramsdale, Stacey, Cook (C), Kelly, Rico, Gosling (L. Cook 69'), Lerma, Billing (Surridge 90'), Stanislas (Brooks 69'), King (H. Wilson 77'), Solanke (C. Wilson 69').
SUBS: Boruc, Simpson, Surman, Danjuma.