The run had begun with victory in added time away to the same opposition in August. This one was much more comfortable and dropped Bournemouth into the bottom three.
Aguero set Pep Guardiola’s team on their way in the 27th minute. Goalkeeper Asmir Begovic lost possession with a poor clearance and Aguero met Fernandinho’s pass with a diving header.
Soon after halftime leading scorer Sterling finished a fine move involving David Silva and Aguero, who then headed his second of the afternoon from a cross by substitute Bernardo Silva.
Danilo, another substitute, scored the fourth within three minutes of coming on to leave manager Guardiola satisfied at having overcome defensive opposition again.
“It was so tough because they play five at the back and 10 players behind (the ball),” he said.
”So space was almost impossible to find and we were lucky to score the first goal. The last 20 minutes they pushed up and after that we played a really good game.
”A good performance and we were ready mentally again.
“Now it’s a merry Christmas and thinking about (playing) Newcastle.”