Joao Cancelo's first City goal opened the scoring midway through the first half, goalkeeper Jordan Archer wrong-footed by a deflection off helpless defender Elliott Moore.
League One side Oxford hit back just after the break, Matty Taylor taking his goal brilliantly to restore a short-lived parity, but Sterling — captain for the night — tucked in Angelino's left-wing centre to put holder City back in front.
Sterling struck again to seal a spot in the last four, with Pep Guardiola's assistant Mikel Arteta on the City bench amid reports the former Arsenal midfielder is set to succeed Unai Emery as the Gunners boss.
Oxford skipper Rob Dickie made a brilliant last-gasp clearance to deny Sterling a tap-in as City turned the screw after a slow start.
The Premier League champion was in front in the 22nd minute with a fantastic team move spanning the length of the pitch, although Cancelo's finish took a big deflection.
Oxford scored a shock equaliser 21 seconds after the interval, Shandon Baptiste sent Taylor clear on the right channel and nutmegging Taylor Harwood-Bellis before steering a low shot past goalkeeper Claudio Bravo.
But within five minutes City led again, Phil Foden freeing Angelino on the left to deliver a low centre that Sterling could not miss.
City's progression was sealed in the 70th minute, Sterling netting his 33rd club goal of the year in all competitions with another close-range finish from Gabriel Jesus' centre, and Cancelo hit the post late on as the gulf in quality finally told.