The Argentina striker opened the scoring after 15 minutes, and Raheem Sterling doubled the lead shortly before half-time. Harry Wilson gave the Cherries hope with a stunning free-kick just before the break, but Aguero hit again in the second half, all but securing the win.
It was his 400th career goal:
Bournemouth started well and got the first shot on goal after just a few minutes, courtesy of a wonderful bit of individual play from Joshua King. The Cherries more than held their own against the defending champions, and Ederson was booked after taking out Callum Wilson with a rash intervention.
City's pressure was relentless, however, and with a bit of good fortune, they took a lead after 15 minutes. A Kevin De Bruyne volley was deflected into the path of Aguero, and the Argentina striker calmly finished from close range.
While he didn't mean to pass the ball, De Bruyne's assist saw him become the fastest to reach 50 in Premier League history:
The goal put City in charge of the match and they went looking for a second, with Bernardo Silva having a dangerous volley blocked. Sterling and Kyle Walker both strayed offside, bringing an end to promising attacks.
Bournemouth's task became even harder when Charlie Daniels went down with an apparent knee injury, and he was stretchered off the pitch:
Six minutes later, David Silva picked out Sterling, who raced ahead and doubled the lead shortly before half-time.
The reigning champions appeared in full control heading into the dressing room, but Wilson handed some momentum back to the hosts with a late goal of his own, a cracking free-kick that gave Ederson no chance.
The substitute is an expert at long-range goals:
The first chance of the second half fell to Sterling, but he just couldn't get to the ball to tap home what would have been his second. Wilson went one-on-one with Ederson but couldn't beat him, and De Bruyne fired wide during the resulting counter attack.
Bournemouth enjoyed a brief spell of dominance just before the hour mark, but that didn't result in major chances. Instead, the Blues doubled their lead after 64 minutes, when Aguero struck again after a second assist from David Silva.
The Spaniard celebrated his 400th appearance for the club:
Whatever hopes Bournemouth had to secure the upset were all but dashed, and the pace of the contest dropped as a result. City had opportunities on the counter, but got careless by straying offside too easily.
Dominic Solanke fired one of the few chances for the hosts right at Ederson, who was rarely troubled in the second half. City easily played out the final minutes to pick up all three points.