Bournemouth started the game well and were first to threaten when King left Otamendi for dead before racing towards the City box, the Norwegian exchanged passes with Adam Smith but his shot was blocked by David Silva.
Nevertheless the cherries continued their strong start, snapping into tackles and refusing to give their more illustrious opponents time on the ball.
They were rewarded for their endeavour after 13 minutes as Charlie Daniels opened the scoring with a sensational strike. Gosling's cross from the left was cleared by Kompany but only as far as the left-back who fired a rasping half-volley into Ederson’s top left corner with a little help from the bar.
Unfortunately for Eddie Howe’s side, that goal only served to wake the visitors up. Raheem Sterling saw a long-range effort easily saved by Begovic before City levelled on 21 minutes.
Jesus was brought down near halfway by Ake and jumped to his feet to take the free kick quickly, he exchanged passes with David Silva with the Spaniard’s reverse ball splitting the Bournemouth defence and allowing the Brazilian to hold of Ake and prod past the onrushing Begovic to equalise.
From then on City took control of proceedings, their full backs often acting as their most advanced players as they probed Bournemouth’s five-man defence.
Ake could have been dismissed shortly afterwards when he dithered on the ball and allowed Jesus to sneak in, before bringing the Brazilian down but Mike Dean opted for a yellow card, much to Pep Guardiola’s ire.
The Brazilian then fired wide at the far post after Mendy’s fine cross from the left before David Silva rifled a volley over the hots’ crossbar as the visitors tightened the screw.
Danilo saw an effort kicked away by Begovic, before Bernardo Silva wasted a great opportunity.
Ake gave away possession cheaply, allowing the Portuguese to drive towards goal but he opted to go alone despite having support left and right and his tame effort was easily gathered by Bournemouth’s Bosnian stopper.
Begovic was forced into action again just before the break to keep the scores level as he just about managed to stop Fernandinho’s rasping effort from a tight angle on the right.
The two sides went into the break level but it felt like a matter of when rather than if City would find a second.
The second half started at a much more sedate pace than the first half finished, with neither side creating a clear-cut chance.
Sterling was crowded out at one end before a timely interception from Kompany prevented Defoe from meeting a cross from the right.
The tempo increased as the game went on, City could have taken the lead just before the hour mark. Bournemouth’s set-piece routine was picked off by the visitors who countered at pace. De Bruyne’s inviting cross from the left was begging to be converted but no blue shirt obliged, much to the Belgian’s displeasure.
Just minutes later Eddie Howe’s men showed that they were still a threat as Josh King sent a left-footed effort goalwards, only to see it rebound back off the post with Ederson beaten.
Bournemouth mounted a brief spell of pressure before City took control again. Sergio Aguero hit the deck shortly after coming on for the ‘citizens’ but Mike Dean was unmoved.
The visitors then fired in a bombardment of half-chances with Fernandinho and Aguero both denied by the impressive Begovic.
When the Bosnian was beaten after 75 minutes the post came to his rescue as Otamendi rose highest to meet a corner from the left and crash a header back off the woodwork.
Silva fired over late on, before Aguero curled a dangerous free kick just wide as the game looked to be heading for a draw.
That was not to be the case, Bournemouth could have won it as Josh King fired an effort at Ederson from range in injury time, despite Lys Mousset being better placed for the pass.
Raheem Sterling proved to be City's hero again in the 97th minute as he gathered Danilo's low cross fromt he right and fired a deflected effort past Begovic and into the far corner to give City all three points. Though Pep Guardiola will undoubtedly be furious with the decision to award the England international a second yellow card for his overzealous celebration.