Erling Haaland netted a first half brace either side of a Tyler Adams goal for the visitors to see the hosts lead 2-1 at the break.
Nico O’Reilly extended City’s advantage on the hour mark and the Cherries were unable to find a way back into a game which the Citizens were then able to control.
The result sees City leapfrog the Cherries into second, with Bournemouth now in fourth.
Andoni Iraola made two changes to his starting XI which defeated Nottingham Forest last week, with Bafode Diakite and David Brooks coming into the side, the latter captaining the team.
Veljko Milosavljevic and Justin Kluivert dropped back to the bench, while Evanilson and Adam Smith returned to the squad and were among the substitutes.
Manchester City's Jeremy Doku (centre) battles for the ball with Bournemouth's Bafode Diakite (left) and David Brooks (right) during the Premier League match at the Etihad Stadium, Manchester. _(Image: Martin Rickett/PA Wire)_
The Cherries made a promising start and had the ball in the back of the net after just a minute as Junior Kroupi turned a Brooks cut back home, but the young Frenchman was just offside.
Haaland had City’s first shot on target of the game from the left of the box, but he fired tamely at Djordje Petrovic and the Serbian caught comfortably.
But Haaland gave the home side the lead after 17 minutes, as he finished when one-on-one with Petrovic after Rayan Cherki’s headed through ball saw the Norwegian race through beyond the Bournemouth defence.
The Cherries were back level eight minutes later, though.
Bournemouth's Tyler Adams (centre) celebrates after scoring his sides first goal during the Premier League match at the Etihad Stadium, Manchester. _(Image: Martin Rickett/PA Wire)_
Alex Scott delivered a corner that Gianluigi Donnarumma flapped at, his punch weak and the ball dropped in the six yard box.
Adams was the first to react and the American finished from close range for his first goal for the Cherries.
City had loud shouts for a penalty waved away after Alex Jimenez blocked a cross with his knee and the ball went into his arm, before City retook the lead with 33 minutes on the clock.
It was Haaland again who was played in behind the Cherries defence once more, he rounded Petrovic and was headed away from goal but he finished well beyond the despairing dive of the Serbian.
Manchester City's Erling Haaland celebrates after scoring his sides second goal during the Premier League match at the Etihad Stadium, Manchester. _(Image: Martin Rickett/PA Wire)_
There was a big chance for the hosts to open up a two-goal advantage as Nico O’Reilly beat Petrovic and shot, but the backtracking Jimenez cleared the ball off the line with Foden threatening behind for a tap in.
Antoine Semenyo saw a shot from distance saved comfortably by Donnarumma before Petrovic made an excellent save to deny Haaland a third – the stopper put a big hand out to save as the striker sought to lift the ball over him.
Petrovic saved superbly again in the final action of the first half, the keeper at full stretch to deny Cherki from a free kick.
The Cherries trailed by one at the interval and the first chance of the second half fell the way of the hosts, as Haaland headed over an O’Reilly cross.
Kroupi fired into the side netting in the first Cherries chance of the half after Brooks cut a Semenyo cross back to the 19-year-old.
Manchester City's Bernardo Silva (left) and Bournemouth's David Brooks battle for the ball during the Premier League match at the Etihad Stadium, Manchester. _(Image: Martin Rickett/PA Wire)_
The Frenchman had another chance minutes later when a good passing move culminated in Scott touching a Brooks pass onto the striker, but Donnarumma was equal to it.
The City keeper saved easily from a Brooks shot from distance, before the hosts extended their lead.
O’Reilly received the ball around ten yards outside the Cherries box and made space for a shot with a feint, before pulling the trigger and finishing low between Senesi’s legs and past Petrovic.
_(Image: Martin Rickett/PA Wire)_
With a two-goal deficit to now overcome, Iraola went to his bench, with Evanilson, Lewis Cook and Kluivert replacing Kroupi, Jimenez and Brooks.
Cherki had the next sight of goal, as he curled the ball over the bar, before Tavernier turned a Semenyo cross wide after a key O’Reilly touch meant the Englishman couldn’t get clean contact on it.
Scott was replaced by Ryan Christie with 17 minutes to play, before Ben Gannon-Doak came on for Adams seven minutes later.
Omar Marmoush poked the ball into the side netting before Petrovic kept out a powerful effort deep into stoppage time.
That Tijani Reijnders shot proved to be the final action of the game as the Cherries were beaten in the league for the first time since the opening day of the season.
**Manchester City:** 25, G. Donnarumma (booked, 26’); 33, N. O'Reilly; 24, J. Gvardiol; 3, Rúben Dias; 27, Matheus Nunes; 14, Nico González; 20, Bernardo Silva (c)(Rodri 90’); 11, J. Doku (Savinho 73’); 47, P. Foden (booked, 45+2’)(Ait-Nouri 90’); 10, R. Cherki (Reijnders 73’); 9, E. Haaland (Marmoush 82’).
**AFC Bournemouth:** 1, Đ. Petrović; 3, A. Truffert (booked, 65’); 5, M. Senesi; 18, B. Diakité; 20, Alex Jiménez (Cook 62’); 12, T. Adams (Gannon-Doak 80’); 8, A. Scott (Christie 73’); 24, A. Semenyo; 7, D. Brooks (c)(Kluivert 62’ (booked 87’)); 16, M. Tavernier; 22, E. Kroupi (Evanilson 62’).