First-half strikes from Albert Mills and Gabriel set us on the way, with our young Reds exerting dominance throughout the opening 45 minutes.
Further goals from Chido Obi and Noah Ajayi completed the scoring at the Kassam Stadium, with Josh Holton notching for the hosts.
We will now play Sunderland or Brighton and Hove Albion in the last eight, with that game to be played by 14 March.
FIRST HALF
It was Oxford who started the brighter of the two sides, with winger Mo Missanga threatening inside the opening 60 seconds. Flying down the left flank, his cross into the six-yard box served as an early eye-opener for United's Academy side.