Pep Guardiola's men cruised into a three-goal lead at the break, looking close to our best in our first home match of the new season.
Kevin De Bruyne added a sumptuous second soon after, curling an effort with the outside of his boot into the bottom corner after carving open some space with a clever drop of the shoulder.
Number three followed just six minutes later when Phil Foden prodded home from close-range.
And the scoring was complete with ten to play when Joao Cancelo's cutback was turned into the Bournemouth net by the rapidly retreating Jefferson Lerma.
Victory leaves the Premier League champions top of the pile after two matches, with Arsenal the only other side still able to boast a 100% start to the campaign.
CITY+ subscribers can watch the best bits of our latest win from our unique Pitcam angle, bringing you closer to the action than ever before.