Joao Cancelo's deflected first-half goal was cancelled out by an equaliser from Matty Taylor.
But the spirited Oxford were eventually overran courtesy of a double from Raheem Sterling.
Speaking after the game, manager Pep Guardiola said: "We play against a top side so congratulations for the team, young players and the victory"
"Everything [pleased me], a lot of games, we now have six or seven in 18-19 days which is tough and the competition itself now is tough, there are quality teams in the semi-finals."
On conceding 18 shots, Guardiola added: "That means they are good. We suffered a lot in the second half. At 2-1 they play long balls with throw-ins, corners and we struggled but it's okay, we knew before we came here."
The Sky Blues will meet neighbours Manchester United in the semi-final first leg on January.