City have won this competition for the past two seasons and Pep Guardiola showed his intent to keep hold of the trophy by naming a strong side.
Joao Cancelo's first goal for the English champions opened the scoring midway through the first half after his shot was deflected by Moore, but City were momentarily stunned when Matty Taylor levelled a minute into the second half after a quickly taken free-kick by Baptiste. Replays showed the goal should not have counted as the ball was still moving when the set piece was taken.
The home side's joy was short lived though as Sterling quickly restored the visitors' lead as he tapped home a wonderful cross from Angelino.
But City were put under intense pressure for a spell and needed Claudio Bravo to make a fine save from Tariqe Fosu's shot.
Guardiola then introduced Gabriel Jesus from the bench in a bid to kill the tie off and it was from the Brazilian's cross that Sterling tapped home his second 20 minutes from time. Cancelo nearly bagged his second a few minutes later, but he was denied by the post and then despite a late Oxford flurry, they were unable to beat a brilliant Bravo in the City goal.
Man City will now face Man Utd in the semi-final over two legs in January while Leicester play Aston Villa in the other tie. Oxford's Carabao adventure ends, but they were by no means disgraced.