Jack Wilshere's ankle injury will be assessed on Tuesday with Bournemouth hoping the midfielder is not facing a lengthy spell on the sidelines.
The midfielder, on a season-long loan from Arsenal, was hurt as he blocked a shot from David Silva and was replaced by Benik Afobe.
It was the second early change Eddie Howe was forced to make after captain Simon Francis had to be replaced by Tyrone Mings in the 23rd minute.
And the Bournemouth manager said both players' injuries would be reassessed on Tuesday.
"Simon just felt his hamstring again on a kick and Jack just had a pain in his ankle, but we will reassess both injuries and hopefully they are not serious," said Howe.
Sterling's sixth goal of the season and an own-goal by Mings secured the win for City. The result leaves Bournemouth 14th in the Premier League and just six points above the relegation zone.