With Premier League leaders Liverpool off to a perfect start with three successive victories, City are already under pressure to keep pace.
Pep Guardiola's side did just that thanks to Aguero as City's record goalscorer hit another milestone with a clinical double in the south-coast sunshine.
Raheem Sterling was also on the scoresheet - making it six goals in four games this term for the England winger - as City's second win of the season lifted them to within two points of Liverpool.
It was a landmark day all round for City, with captain David Silva involved in all three of the goals on his 400th appearance for the club.
"We felt Bournemouth's physicality, a nice three points and a big compliment to the players, a few things to improve, that's good it's happened when we are winning games," Guardiola said.
- Relief for Bruce -
Meanwhile, Steve Bruce silenced his critics as Newcastle won 1-0 at Tottenham to secure their first points under the new Magpies boss.
Since taking over from Rafael Benitez in the close-season, Bruce had found himself under pressure after losing his first two games, with fans doubting his credentials and former players claiming his squad were uncertain about his methods.
But Joelinton's first goal for Newcastle in the 27th minute gave Bruce some breathing space for a few days at least.
Davinson Sanchez was caught playing the offside trap, allowing Brazilian forward Joelinton to collected Christian Atsu's inch-perfect ball and fire home.
"We have tried to quieten the storm. Hopefully that will shut a few people up a little bit. After two games, it's been hard to get that criticism. We have had to ride it," Bruce said.
Newcastle were helped by a poor performance from Tottenham, who have won only once in their first three games.
Mauricio Pochettino's side were frustrated by VAR after the decision-review system did not award a penalty when Harry Kane tumbled under a challenge from Jamaal Lascelles.
"We didn't perform as we expect. It was a very cheap goal. I'm very disappointed with the performance and with the result," Pochettino said.
Tottenham playmaker Christian Eriksen was only used as a substitute amid uncertainty surrounding his future ahead of the European transfer window shutting next week.
"I am going to be happy in 10 days after we play Arsenal when the transfer window closes in Europe," Pochettino added.