The Cherries had frustrated City until Asmir Begovic’s poor clearance led to Fernandinho finding Aguero to nod the home side in front.
Raheem Sterling made it 2-0 at the start of the second half when Aguero deftly flicked the ball over the visitors’ defence for him to gallop in and slot home.
Aguero added a third with another header, this time from a Bernardo Silva cross, for City’s 100th league goal of 2017.
Danilo completed the rout with five minutes to go when he ran on to Sterling’s pass to score his first goal for the club.
City’s victory extended their lead at the top of the table to 14 points, at least until second-placed Manchester United play Leicester later on Saturday (19:45 GMT).
Bournemouth, who are now without a win in their past seven league games, slip into the bottom three.
Eddie Howe’s side were the opposition when City began their winning run back in August – on a sunny day on the south coast, when it took a 97th-minute Sterling goal to defeat them.
Now, 119 days on and with Santa hats in the stands at Etihad Stadium, there is still no stopping Pep Guardiola’s side.
They have reached the halfway stage of the season and have dropped only two points, while the teams immediately below them continue to falter.
