Kevin de Bruyne put the league leaders in front with a low free-kick under the wall after a Jack Wilshere foul.
City were dominant and two sweeping counter-attacks led to Kelechi Iheanacho and Raheem Sterling tap-ins.
Ilkay Gundogan calmly slotted in a fourth but City had Nolito sent off late on for an attempted head-butt.
The Spaniard was involved in a clash with Adam Smith and, while any contact with his head looked slight, referee Jon Moss had little option but to dismiss the winger.
Deadly De Bruyne
City's passing and movement was a joy to watch and the influential De Bruyne was at the heart of their play.
The Belgian midfielder, who scored in the win over against Manchester United last week, played behind main striker Iheanacho and caused Bournemouth all sorts of problems as he was involved in all his side's goals before going off to a standing ovation.
De Bruyne's absence for two months last season was a huge setback for City as they dropped from second to fourth in the Premier League, and from three points behind leaders Leicester to 12.
The 25-year-old's intelligence, running with the ball and vision made him a constant threat and his link-up play with Sterling, Nolito and Iheanacho left Bournemouth bemused.
"The performance from Kevin was terrific, amazing," said City boss Pep Guardiola. "He is on another level. He is a fantastic player and helps us a lot."
The rebirth of Sterling
Raheem Sterling did score a hat-trick against the Cherries at the Etihad last season but, for the most part, was a subdued presence following his £49m move from Liverpool.
However, the 21-year-old appears to be back to his livewire best as he closely pushed De Bruyne in the man of the match stakes.
The dribbling skills and pace that make him such a threat were impressively on show against Bournemouth and he has clearly benefited from the arrival of Guardiola.
The City boss phoned Sterling during the summer before officially taking over to tell the winger he was a big part of his plans, and the Spaniard looks to have restored his confidence.
Apart from his goal, and his assist for Iheanacho, Sterling also went close when he dispossessed Charlie Daniels on the right flank, producing a mesmerising run across the Cherries box - past a host of defenders - before seeing his shot hit the post.
Source: bbc
