First half efforts from Aguero and Raheem Sterling ensured Pep Guardiola's side led at the interval despite a stunning free-kick reply from Bournemouth's Harry Wilson.
Argentina striker Aguero wrapped up City's second Premier League victory of the season with his second goal of the game after half-time.
It was Silva, though, who was the architect of the win and having already announced this will be his last season at the Etihad Stadium, this display only underlined how much he will be missed.
The Spanish midfielder remains an integral part of Guardiola's team, with his contribution to City's goals demonstrating exactly why he is so valued by his manager.
For the 15th minute opening goal, it was Silva who operated as the fulcrum towards the start of the move with the midfielder finding Oleksandr Zinchenko on the left, allowing the left-back to drill in the low cross that eventually led to Aguero's finish.
Silva's contribution to the second was even more eye-catching, with his superbly weighted ball picking out Sterling's darting run into the box before the England attacker struck past keeper Aaron Ramsdale.
Then a positive surge into the Bournemouth area caused confusion among the home backline before Aguero pounced for the third.
Those moments helped City maintain control of a game that could easily have slipped from their grasp had Eddie Howe's side enjoyed better fortune.
Aguero's predatory finishing was the perfect tonic for City after Brazil striker Gabriel Jesus was withdrawn from the squad with a hamstring problem sustained in training.
City said Jesus will be back to full fitness after next month's international break, meaning he should miss only next weekend's clash with Brighton.
Bournemouth had established an unwanted record in the corresponding fixture last season when they became the first home team not to register a shot on goal in the Premier League.
- Note of panic -
On this occasion a positive start ensured they quickly avoided a repeat with Josh King testing Ederson in the first minute.
It was clear from the start Bournemouth were anxious not to concede territory to Guardiola's team, who initially appeared unsettled.
Kyle Walker was booked for a foul on Nathan Ake in the 10th minute, having already been fortunate to escape a caution for an equally bad challenge on the same player.
And there was an uncharacteristic note of panic in the City defence when Ederson raced out to the right hand touchline and halted Callum Wilson with a crude, waist-high challenge which also earned a yellow card.
Aguero's strike ended Bournemouth's bright opening, with the forward reacting first after Kevin De Bruyne miscued from Zinchenko's shot.
Bournemouth responded well, despite losing left-back Charlie Daniels to a knee injury and would have levelled but for Ederson's fine save to deny Ake shortly before the keeper produced an even better block from Adam Smith's close-range shot.
Belief was growing among the hosts before Silva's second major contribution when he teed up Sterling to double the lead two minutes before the break.
And the intervention was particularly timely as moments later Harry Wilson, on for Daniels, brought Bournemouth back into the game with a stunning free-kick.
The goal ensured Bournemouth returned from the interval full of hope, with Wilson drawing another fine save from Ederson.
City were convinced they should have had a penalty when Silva went down under a challenge from Jefferson Lerma, but the referee Andre Marriner decision to ignore the visitors' claims was upheld by VAR.
Perhaps aggrieved at the decision, Silva wasted no time in setting up Aguero's second goal to ensure Guardiola's side eased their way to victory.