Aguero, who has scored in all three games this season, gave City a 15th-minute lead.
The striker slotted home after left back Oleksandr Zinchenko’s low cross had been mis-hit by Kevin De Bruyne only to fall kindly for the Argentine.
Adam Smith then missed a great chance to level for the Cherries, firing high over the bar from a good position after some poor defending from Nicolas Otamendi.
Moments later Raheem Sterling doubled City’s lead with a confident finish after David Silva concluded a sweeping move with a perfectly angled pass to the England striker.
But Bournemouth got back into the game in magnificent fashion, just before the interval, thanks to an unstoppable curling free-kick from substitute Harry Wilson, on loan from Liverpool.
Wilson went close to a leveller after the interval but Ederson was out quickly to foil his effort.
City then made sure of the win when Aguero poked home his second goal in the 63rd minute, following in for the scraps after David Silva had surged into the box. (Reuters/)
Edited by Felix Ajide